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# what do you get when you add all of the numbers from 1 to 100?

what do you get when you add all of the numbers from 1 to 100?

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You pair them off:

1+99 = 100

2 + 98 = 100

3 + 97 = 100

...

48+52 = 100

49 + 51 = 100

That's 49 pairs of 100. We accounted for everything but the 50 and the 100. So 49*100+100+50 = 5050.

This is a problem famously solved by C.F. Gauss when he was a child. See:

http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#...

There is a general formula for this:

http://en.wikipedia.org/wiki/Arithmetic_series#Sum...

1 + 2 + ... + n = n(n+1) / 2

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• Sn = n(n + 1)/2

with 1 + 2 + 3 +... + n

So, 1 + 2 + 3 + ... + 100 => 100(101)/2 = 5050

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• it is A.S a=1,l= 100 ,n=100 then sum = n/2 (a+ l) then

sum = 100/2 (1+100)=5050

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• You have 100 numbers.

Average = 101/2 = 50.5

50.5 x 100 = 5,050

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• Anonymous

5050

the formula you can use to calculate "n" for any number is

1/2n^2+1/2n

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• 5050, just like Gauss did!

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• 5,050.

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