maths

Posted December 13th, 2007 by Anonymous

sum of odd natural numbers from 1 upto 2n-1

Comments

On December 13th, 2007 Structure says:

We have

$S_n=1+3+5+.....(2n-3)+(2n-1)$

but also

$S_n=(2n-1)+(2n-3)+ ...3+1$

Summing up

$2S_n=(1+(2n-1))+(3+(2n-3))+...+((2n-3)+3)+((2n-1)+1)=2n+2n+...+2n+2n=2n^2$

We have finally

$S_n=n^2$