How to add 1 through 100 quickly

► My Pre-Algebra course: www.kristakingmath.com/prealg...
If you want to add up all the numbers 1 through anything, like 1 through 100, or 1 through 23, there’s actually an easy way to do it. You might think you’d have to grab your calculator and manually add up 1+2+3+4…, all the way until you get to your ending number. But there’s a much faster way to do this addition problem; it’s by turning it into a multiplication problem.
If you’re adding the numbers 1-n, the quick trick is to use the formula (n/2)(n+1). So if for example you’re trying to add up all the numbers 1-64, then you know right away that the sum of all those numbers is (64/2)(64+1)=32*65. As you can see, the tedious, time-consuming addition problem becomes a simple multiplication problem.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@joshuaaa3337]

wOW. i am studying segma in calculus, and just after watching this video, i understood how the pattern of n was done for the sum of numbers. great teacher.

[@ericmcdowell5762]

We were posed this question by my Math teacher in HS, and I had never heard of Gauss, or his equation, but came to the same conclusion, ... and wrote down 5050 on a piece of paper, while the rest of the class was doing long-hand addition. They were all surprised when the teacher walked over to my desk, and shook his head "yes", as he knew of my abilities. I constantly got over 100 on his tests, as he would give "extra credit" questions. He had me go to the front of the class, and explain how I came to the conclusion I did, so quickly, on the blackboard.

[@AmCanTech]

luckyt

[@kristakingmath]

Here’s an easy way to add up all the numbers 1-anything!

[@ankitbisht7]

Krista King ty

[@thewizardii1638]

thanks..

[@joebabycarrol]

I am by no means good at math, but I got lucky and found a another way to solve this. I go by fives. It doesn’t work for five itself but after that 10, 15, 20, etc. it does. 2.5 is the thing in common. So to find what 1-10 added together equals, you you would add 3 plus 2.5 and that’s 5.5 times the number your looking for (which is ten) so that equals 55. For 15, you now take that 5.5 and add 2.5 to it to get 8 and multiply that by 15 which is 120. Take that 8 and add 2.5 to get 10.5 and multiply that by the next 5 in the series which is 20. And you get 210, which is what 1-20 added together equals.

[@music-lu4xg]

Interested in proving new chemical formulas what type of PhD and who is good to determine outcome or even quality

[@saidmohammad1270]

99samriankhan

[@andylipscomb5199]

Thanks. I was watching Person of interest and Guess along with this math problem I did a search and your video came up. You explained it very well. I had no problem following it. Though I may have to watch a few more times so it sticks.

[@alexandraasbury9974]

same here, exactly!!

[@bishalpoudel481]

hi krista I am very inspired from your videos and made me very easy to understand maths (calculus) thank you very much

[@kristakingmath]

Glad I could help. :)

[@bhagatcharan1127]

thank you sister for ur excellent math videos

[@unclet6810]

Now that was a simple explanation.

[@damyb9db]

I'm subscribing to you just because of how easily you explained this!

[@kristakingmath]

Thank you so much, Damian, I'm so glad you enjoyed it! :)

[@Froggie1337]

I learned to do this a little different and with other numbers not just starting from 1 to 100, you can do any number be it 57 to 183 or 197 to 26,392. So let's say you want to add up all the numbers from 75 to 150. You take the 1st and last number and add them together, 75+150=225. Then you need to find out how many number there are from 75 to 150 , for that you can simply do 150-75+1=76 (75,76,77,78 etc.). Then you take those 2 numbers, 225 and 76, you do 225x76/2 and you got your answer. 8,550 Correct?

[@margienava9940]

Very explainable, need to really concentrate on this a little longer, an I'll get it,,? Very interesting!! I luv learning, going to practice until I get it ? Thx alot....😍👍😘

[@Froggie1337]

​@@margienava9940 You're very welcome. I would say try it with small numbers, like 1 to 4. Get a feel for how it works. Add them together, 1+4=5. How many numbers are there between 1-4? 1,2,3,4 or like I said 4-1+1=4 (You always have to +1 to this part, I don't remember why but I've always done it this way). That's 4 numbers, so then you take 5x4/2. 5x4=20, 20/2=10. 1+2+3+4=? 10!!! Remember you can do this with any numbers, 5-10, 136-360. Give it a try, I would love to hear/see what you come up with...

[@ugadugaga4972]

Omg thank you. I bought a book and read this but had no idea where the 101 came from. Multiple websites with different explanations but the moment I saw you write it out it made total sense.

[@alexandraasbury9974]

Ah, wonderful help. I learned about Gauss and this, and you explained it perfectly!! Thank you.

[@chandranneves972]

Hi

[@miniclipday]

You can also think of it as calculating the area of an trapezoid. A = 1/2 * (sum of top and bottom) * h So in sum of 1 to 100, top is 1 bottom is 100, and h = 100. so A = 0.5*(1+100)*100 = 101*50 = 5050

[@alexandraasbury9974]

well done!

[@joebabycarrol]

I am by no means good at math, but I got lucky and found a another way to solve this. I go by fives. It doesn’t work for five itself but after that 10, 15, 20, etc. it does. 2.5 is the thing in common. So to find what 1-10 added together equals, you you would add 3 plus 2.5 and that’s 5.5 times the number your looking for (which is ten) so that equals 55. For 15, you now take that 5.5 and add 2.5 to it to get 8 and multiply that by 15 which is 120. Take that 8 and add 2.5 to get 10.5 and multiply that by the next 5 in the series which is 20. And you get 210, which is what 1-20 added together equals.

[@akramkhanafridi1755]

Excellent explanation

[@kristakingmath]

Thank you so much! :)

[@ankitbisht7]

wow you encourage me towards mathematics

[@Ajaykumaraita]

maam can you do advanced topology video lectures...

[@joe-emcator6420]

Wowww thanks for the learning 😍

[@kristakingmath]

You're welcome, I'm happy to help! :D

[@ben78412]

we multiply then divide ex: 100x101=10,100 / 2 = 5050

[@ben78412]

works on finding the SUM of

[@ugadugaga4972]

Question. Say if you started with an odd number, does it work the same?

[@sfwx4]

Yes

[@alexandraasbury9974]

yep.

[@amyers01]

This is fine as long as n is positive. May as well take n(n+1)/2. To me that's easier.

[@thewizardii1638]

so is 1-101. n divide 2.1 and n plus 2..say example 61 30.5 divide 2.1.. and 31 plus 2. which ever answer these two are x by for answer??..

[@thewizardii1638]

x is times by..

[@nickw22689]

Great video, but after explaining it the long way, would have been a good idea to mention the formula - "n over 2 times n plus 1". n over 2 times n plus 1

[@AmCanTech]

cool!!

[@alfredtison5288]

I found this fun!

[@kristakingmath]

Awesome, Alfred! Glad you enjoyed it! :)

[@Fake-eo4mx]

I like your video because that would be part of my exam

[@kristakingmath]

Glad it helped! :)

[@Hasui17]

on my side what i do is its kidna simmilar but I settle at 100. 1+99, 2+98 and etc then 4900 at total and there the left in 50 and 100 so add them to 4900

[@Sunshine48541]

We can also do this by arithmetic progression .

[@user-fy5fe6vr8p]

글씨가 예쁘고 목소리가 좋네요 ^^ 얼굴도 예쁘시고 종종 보고 갑니다 좋은 하루되세요

[@johncloois3301]

Narration. ❤️

[@Noneblue39]

i remember when this problem was impossible for me!😩

[@onurolce]

1 + 2 + 3 = 6 n = 3 (n * (n + 1)) / 2 (3 * (4)) / 2 = 12 / 2 = 6 so formula is ; sum = n * (n + 1) / 2

[@onurolce]

dividing n can be decimal results which is harder to calculate, therefore my formula is more easier :)

[@onurolce]

yeah sure. everybody has different style of eating of yoghurt :)

[@nirmalabenbagda3875]

This a long thing I have right way

[@pammitiwari3416]

So bad because I have a non minus plus

[@cailynswaisgood2436]

Hi what are you doing what are you doing what are you doing what are you doing

[@Terbie36]

Looking at the number of likes, I see that Maths is the devil' doing.