Summations (sigma notation) is used to represent a large sum of terms that follow a pattern. In calculus you will learn about series, which are sums with an infinite number of terms. But before you get to that, you need to understand the basic notation.

A common example provided in the video is the sum of 1 through 100. Also, a short introduction to the sum of 1 through some positive natural number n is discussed.

0:00 Introduction
0:09 Basic components of summation notation
0:37 Basic Example: Summing i from 1 to 3
1:27 How summation notation compacts large sums
1:56 Example: Summing i^2 from 1 to 5
2:43 Summing natural numbers from 1 to n
3:50 Using closed form solution to sum from 1 to 100
4:40 Warnings for things I didn't talk about
4:45 Any letter can be your index of summation
5:10 You can have a sum of variables
5:33 You can sum over sets
6:03 Hammering in the message

#summation
#sigmanotation
#sums
#joecmath
#calculus

Short, edited, easy to follow math tutorials for high school and college subjects. Consider watching some videos and subscribing to support the channel!

#maths
#mathhelpers
#joecmath
#mathchannel
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#collegemath

It's Kids Academy, and welcome back to our channel! In this educational video for kids, we will learn letters U, V, W, X. Your child can easily memorize letters I to L using our examples. It's ideal for preschool and kindergarten. Stay tuned!

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It's Kids Academy, and welcome back to our channel! This number song is easy to sing and chant along. Kids will have fun following the characters and counting 1-10 with them. They won't be distracted by unnecessary details. A great educational activity for preschoolers and young learners. Enjoy your viewing!

Try Kids Academy now! Enjoy our special Cyber Week offer. The price was 75% higher! https://clck.ru/YuJaw

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Baby Shark is the most popular kids show in the world and for good reason! This hilarious and heartwarming show is perfect for children of all ages. Baby Shark by Kids Academy will have you singing and dancing along with your kids!

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It's never been so easy to teach your child how to match different colors, clothes, etc. Learn how to sort and match easily with our new video.

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Learn the Letter G | Alphabet for Kids | Kids Academy

We all know the alphabets from A to Z but, we find it difficult to learn the alphabet letter G. We help you earn alphabet easy. A lot of kids do not pronounce the alphabet letter G correctly, and it affects their pronunciation and enunciation in the long run.
Learning the alphabet letter G is fun.

If you want to know how to learn the alphabet, we can teach you to pronounce the alphabet letter G quickly and easily. We use pronunciation guides, videos, and speak along tutorials to excel at learning the alphabet letter G. You will have fun in learning and pronouncing the alphabet letter H with us.

We also teach examples using the alphabet letter G. We use a fun and interactive method to teach the alphabet letter g to our students.


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Kids Academy Talented and Gifted Program for kids aged 2-10:

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The fourth Thursday of November is a special day in some countries because that’s when people celebrate Thanksgiving. On this day, families get together and share a holiday meal. In our new video, Nancy will share with your kids how they usually celebrate Thanksgiving in her family and why she loves this holiday. You’ll find out what fun activities they engage in, what food they eat and what things they are thankful for.

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Learn to Play Chess - Discovered Attack | Kids Academy

The discovered check can help you win the game. It is one of the most intelligent moves in chess. This move will make your opponent come out of their comfort zone and move their king. This would block the check of your opponent, which means that your chances of doing checkmate increases and you can put the opponent’s king under threat. It is one of the most common played tactics in chess.

So, what happens in this kind of move is that when you move a piece, a piece is revealed behind it that is now attacking the king. This will force the opponent to move their king hence giving you a chance to checkmate. A discovered check is one of the most popular moves used in chess and very important to the lesson for chess for beginners. It can help you earn a lot of points and win the game.


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It's Kids Academy, and welcome back to our channel!

What’s the weather?

In today’s technology-laden world we can start the day by simply asking our digital assistants “What’s the weather going to be today?” But weather goes far deeper and can be far more interesting than just whether or not you are going to put on a jacket today. We are going to explore the fascinating world of weather and show fun ways you can interact with the weather every day!

Let’s start with what the weather is. Weather describes the conditions outside at any given time. This usually includes the temperature, if there are any clouds present and, the reason most of us check it, will there be any rain?
Let’s start with temperature. The temperature can tell you how hot or cold a day is going to be. In the United States we use the Fahrenheit scale. This scale is hundreds of years old and was based on human beings internal temperature being roughly 90 degrees fahrenheit. A thermometer is the device used to measure temperature. As technology improved and thermometers advanced we learned that a human body’s internal temperature is actually closer to 98 degrees fahrenheit than the 90 degrees that the scale was built off. The rest of the world, excepting Liberia and the Cayman Islands, uses the celsius scale. This scale is based on the freezing and boiling temperatures of water.
One of the questions students always ask me is “If I am 98 degrees then why does a 98 degree day feel so hot?” The answer to this question is all about the skin. When we take our temperature we usually put the thermometer in our mouth to get our internal body temperature. If you were to take the temperature of your skin it would be closer to 70 degrees. That is why we feel comfortable around that temperature and get hot or cold if the temperature goes above or below 70.
Our next big concern with weather is what is going on in the sky. Clouds can quickly turn a hot morning by the pool into a chilly afternoon. Clouds are made of evaporated water. As the sun heats oceans, lakes and even pools some of the water heats up enough to evaporate. This evaporation is what causes rain puddles to disappear when the sun comes out. The water warms and rises into the air until it reaches the colder parts of our sky. When the water cools down it condenses or sticks together, just like on a cold mirror in the bathroom after you take a hot shower. As the water sticks together it can form all kinds of different clouds. If enough of this water sticks together it can become too heavy and fall back down to earth.
Any water coming out of the sky is called precipitation. Precipitation can come in many forms. One of the most common forms is rain. As the tiny drops of water in clouds collect they will form raindrops, these drops fall through the cloud picking up more and more water on their way down. Sometimes raindrops can be small and misty, other times the drops can be huge and hit with a splash. If the temperature is cold enough these raindrops can freeze on their way down causing freezing rain, sleet and hail. If the cloud is cold enough the water freezes into ice crystals which fall as snow.
How can we interact with the weather? Grab a thermometer and head outside. Start by trying to guess what the temperature is before checking the thermometer. Set the thermometer down in a sunny spot and a shady spot. How do the temperatures differ when they're in the sun?
Make your own predictions. Head outside in the morning, look at the sky and guess or measure the temperature. What do you think the weather is going to be? Will there be rain, or is it going to be sunny all day? Write your predictions down and check to see if you were correct later on. Pretty soon you will be predicting the weather like a true meteorologist. (Scientist who studies the weather, not meteors.)
You can also build a rain gauge. A graduated cylinder works perfect but a cylindrical cup will work just fine. Put out your rain gauge before the rain and then measure how much rain fell by putting a ruler in the cup after. The number of inches of water in your cup is the number of inches of rain that fell during the storm. Did you know every 1 inch of rain would be 1 foot of snow if the weather was cold enough?
Weather is also not a local occurrence. A rainstorm in your area most likely formed hundreds or thousands of miles away. Many of these storms, like hurricanes, follow predictable paths. Using sites like ventusky.com you can track these storms as they begin forming hundreds of miles out in the ocean. You can also get a more global look at weather patterns.
We make a lot of decisions based on the weather. Most students just look at the weather as something that happens without spending a lot of time really thinking about what causes rain or where snow storms come from. Take some time with your student to observe, predict and even measure your local weather.

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Pushing and Pulling | What is the difference? | Force and Energy for Kids

We have seen adults confused between push and pull for their whole lives. This happens when the concept from childhood are weak. So, if you don’t want your kid to pulling a door that clearly says PUSH, you must make the difference crystal clear to them.

Before that, we need to learn some other concepts too, which is about force and energy. Whenever an object is moving we say that it is in motion and to put an object in motion some force needs to be applied to it.

Force is the energy that enables the object to move. Now this force can be either push or pull.
The key difference between push and pull is that we when we apply force on an object to move it away from ourselves we say that we are pushing it. However, when we apply force to move the object towards us we say that now we are pulling the object.

The object will stay in its place unless or until an external force is applied to it which forces it to move and change its position.
After explaining the theory, you can use some real-life examples to further clear out the concept by pushing and pulling different things and asking the kid to identify the kind of force.
This concept can save your kid from banging into many doors trying to push it when it says pull. So, keep it crystal clear.

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Welcome to watch our videos 歡迎觀看我們所創作的其他影片

1）Basic Conversation 會話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

2) Grammar 語法 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

3）English Speaking https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

4）Funny Jokes 笑話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

5）Vocabulary 詞彙 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

6）English Idioms 英語成語 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

7）Revision Exercise 重温練習 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

8）Fun Games 趣遊戲味 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

9） Tongue Twister 繞口令 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

10）Writing a composition 作文 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP
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Daily revision 17_Comparatives Superlatives_BGM info
Candy by Sakura Girl | https://soundcloud.com/sakuragirl_official Music promoted by https://www.chosic.com/free-music/all/ Creative Commons CC BY 3.0 https://creativecommons.org/licenses/by/3.0/

#nature #english #englishfun #vocabulary #温習 #revision #學英文 #英語語法 #英語初學者 #刻意練習 #englishlearning
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今日帶大家親親大自然！一邊行一邊學英文！
影片後半部份，再考一考小朋友，看看是否記得那些植物及動物的名稱？

👇影片主要分為2個部份
00:23 跟我讀(學習詞語部份)
01:48 遊覽大自然(挑戰物件及動物名稱部份)

Welcome to watch our videos 歡迎觀看我們所創作的其他影片

👉🏻1) Basic Conversation 會話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻2) Grammar 語法 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻3）English Speaking https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻4）Funny Jokes 笑話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻5）Vocabulary 詞彙 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻6）English Idioms 英語成語 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻7）Revision Exercise 重温練習 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻8）Fun Games 趣遊戲味 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻9） Tongue Twister 繞口令 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻10）Writing a composition 作文 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

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#tonguetwisters #shorts

I scream, you scream, we all scream for ice cream.

Here are some other videos talking about Conversation.
以下是有關對話的影片：
Talking about playing PIANO | Basic Conversation Lesson 18 | https://youtu.be/a-IODSIb5Z0
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Welcome to watch our videos
歡迎觀看我們所創作的的其他影片
1）Basic Conversation 會話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

2) Grammar 語法
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

3）English Speaking
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

4）Funny Jokes 笑話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

5）Vocabulary 詞彙
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

6）English Idioms 英語成語
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

7）Revision Exercise 重温練習
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

8）Fun Games 趣遊戲味
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

9） Tongue Twister 繞口令
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

10）Writing a composition 作文
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

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Job_What do you want to be when you grow up
Video by Pixabay: https://www.pexels.com/video/d....ata-encrypting-85432
Video by fauxels: https://www.pexels.com/video/p....eople-in-a-meeting-3
Video by Mikhail Nilov: https://www.pexels.com/video/a....-veterinarian-checki

Here are some other video talking about sleep.
以下是其他有關睡眠的影片：
Short phrases about sleeping | English Speaking | https://youtu.be/KQY-J0ce82o
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Welcome to watch our videos
歡迎觀看我們所創作的的其他影片
1）Basic Conversation 會話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


2) Grammar 語法
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


3）English Speaking
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


4）Funny Jokes 笑話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


5）Vocabulary 詞彙
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


6）English Idioms 英語成語
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


7）Revision Exercise 重温練習
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


8）Fun Games 趣遊戲味
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


9） Tongue Twister 繞口令
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP


10）Writing a composition 作文
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

Here are some other videos talking about Conversation.
以下是有關對話的影片：
15 Classroom Language | Basic Conversation Lesson 30 | https://youtu.be/P4daNnAX2YY

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Welcome to watch our videos
歡迎觀看我們所創作的的其他影片
1）Basic Conversation 會話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

2) Grammar 語法
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

3）English Speaking
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

4）Funny Jokes 笑話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

5）Vocabulary 詞彙
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

6）English Idioms 英語成語
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

7）Revision Exercise 重温練習
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

8）Fun Games 趣遊戲味
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

9） Tongue Twister 繞口令
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

10）Writing a composition 作文
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

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Please SUBSCRIBE to our channel, LIKE, and SHARE to encourage us to share more useful and interesting knowledge.
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Please SUBSCRIBE to our channel, LIKE, and SHARE to encourage us to share more useful and interesting knowledge.
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📍📍Welcome to watch our videos📍📍
歡迎觀看我們所創作的的其他影片
1）Basic Conversation 會話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

2) Grammar 語法
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

3）English Speaking
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

4）Funny Jokes 笑話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

5）Vocabulary 詞彙
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

6）English Idioms 英語成語
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

7）Revision Exercise 重温練習
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

8）Fun Games 趣遊戲味
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

9） Tongue Twister 繞口令
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

10）Writing a composition 作文
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

#1minutevideo #englishfun #englishlearning #question #温習 #revision #學英文 #英語語法 #英語初學者 #刻意練習 #english

今天的短片，有5條關於動物的有趣問題，你答對了幾多題？
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Welcome to watch our videos 歡迎觀看我們所創作的其他影片

👉🏻1) Basic Conversation 會話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻2) Grammar 語法 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻3）English Speaking https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻4）Funny Jokes 笑話 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻5）Vocabulary 詞彙 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻6）English Idioms 英語成語 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻7）Revision Exercise 重温練習 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻8）Fun Games 趣遊戲味 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻9） Tongue Twister 繞口令 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

👉🏻10）Writing a composition 作文 https://www.youtube.com/playli....st?list=PLPoPxSDq_eP