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

Write the sum in 2 ways:
\[1+2+3+\ldots+999\]\[999+998+997+\ldots+1\]and notice that the sum of 2 numbers that are on the same vertical is the same for any vertical
\[(1+999)=(2+998)=\ldots=1000\]Just add them using this hint. If you understood what i had written you will have no problems with getting the sum.