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=(1+999+2+998+\ldots+999+1)/(2)=\\ (999\cdot1000)/(2)=999\cdot500=499500`

b)

`1+2+3+4+\ldots+997=(1+997+2+996+\ldots+997+1)/(2)=\\ (997\cdot998)/(2)=997\cdot499=497503`