Problema Solution

Use Gauss's approach to find the following sums

A. 1+2+3+4+...+999

B. 1+3+5+7+...+997

Answer provided by our tutors

А.

S = 1+2+3+4+...+999

S = (1 + 999) + (2 + 998) + ... + (499 + 501) + 500

S = 499*1000 + 500

S = 499,500

B. 

S =  1+3+5+7+...+997

1 = 1 + 0*2

3 = 1 + 1*2

5 = 1 + 2*2

...

997 = 1 + 498*2

S = 498*1 + 2(1 + 2 + 3 + ...+498)

S = 498 + 2*(498/2)*499

S = 249,000