Question

use Gauss's approach to find the follwoing sums (do not use formulas).
a... 1+2+3+4+...+999
b... 1+3+5+7+...+997
the sum of sequance a is...
the sum of sequance b is...

Answer 1

a)
$1+2+3+4+\ldots+999=\dfrac{1+999+2+998+\ldots+999+1}{2}=\\ \dfrac{999\cdot1000}{2}=999\cdot500=499500$

b)
$1+2+3+4+\ldots+997=\dfrac{1+997+2+996+\ldots+997+1}{2}=\\ \dfrac{997\cdot998}{2}=997\cdot499=497503$