Question

to verify that the sum of 'n' natural numbers is n^2

Answer 1

Answer:

The first one uses the formula Σni=0i=n(n+1)2 and the fact that every odd number is of the form 2n−1 :

Σni=1 ( 2i−1)=−n+2Σni=0i

−n+2Σni=0i=−n+2n(n+1)2

−n+2n(n+1)2=−n+n2=n=n2