Question 703760: Hello, I need help to find the sum of the first 500 integers.
I know that the answer is 125,500 and that I need to add 500 to 1, 499+2, 498+3, 497+4, 496+5...and then to multiply by 250 (500/2), but how to put it into a formula that works for all numbers in the row, so that the sum is always 125,500?
The formula S=n(n+1)/2 works only for 500: S=500(500+1)/2=125,500, BUT
if S=499 (499+1)/2, it doesn't work.
Please help!
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Try the formula carefully to see that it works for both values.
n=499,
S=499(499+1)/2
=499(500)/2
=499(250)
=124750
n=500,
S=500(500+1)/2
=250(501)
=125250
Difference is 125250-124750=500.
The formula works for both values of n.
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