Art of Problem Solving: Sum the Numbers from 1 to 100

[rwharrington]

It's astounding the value you can pick up when you solidify the fundamentals of a topic you *think* you understand so well. The typical "gloss-over-the-fundamentals" approach to learning stuff will leave you hamstrung in your journey to the mastery of any complex subject.

[Zacofdeis]

once again, math chad is making math easy

[keir]

Love Guass' idea.

Personally my immediate thought was: okay, I can do 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 to get 45. And there are definitely 10 sets of these 1 to 9s so that 450. Next we have all the tens left over from the 20s, 30s, 40s, etc. This must just be 10 times more than the result we got the for the 1-9s, which is 4500. 4500 plus 450 = 4950. Add the 100 you haven't counted yet, 5050.

[shaneraja]

Such a simple and great explanation cheers thanks!

[illustranimator]

This problem has been bugging me since I was a kid in elementary school trying to comprehend the poor explanation I had from my teacher. This completes one of my bucket list items :). 101x50 because of pairing...yes!!!! and Thanks!

[Mag-Mag]

instead of 101, you can also do 100x50 because 1+99, 2+98 etc. Then add the spare 50 and 100 that did not get paired 😊

[Alkatraz]

Do u think this will work with odd numbers? 1+2+...+8+9
1+9=10
2+8=10
9/2=4.5
4.5×10=45
1+2+3=6
4+6=10
10+7=17+8=25+8=36...?

[popsemdowh]

wow i did not think of that. thank you!

[adorebarbienotme]

can you do this with any number? for example between 1 and

[ilikevines]

n(n+1)/2 is the usual equation, right?

[jakehunter]

Or pair 1-99, 2-98 and get all easy numbers 100+100+100 all the way till you get to 50. You add the 100 since you didn't pair it yet. And pair it with the 50 and bam. Easier way to get to 5050

[jonasgaballa]

I got this question, can some one help me? : What is the sum of the first hundred integers ?
(1 + 2 + 3 + ... + 100 )

[AyushiYadavblithechinku]

great!! now it will be easier thanks a lot !! :) :)

[lakshsharma]

the 6 dislikes are probably from khan academy

[hujgosu]

couldn't you do 0+100, 1+99，2+98 . . .?

[ting-trne]

bro how about making 100 1+99 2+98 3+97....

[johnpaterson]

My way was faster. I should have been a mathematician :(