# The sum of the $n$ smallest odd numbers is equal to $n^2$ [duplicate]

if given a positive integer $n$ is the sum of the $n$ smallest odd numbers equal to $n^2$

## marked as duplicate by user147263, Fly by Night, Blue, achille hui, voldemortAug 27 '14 at 0:05

• Base case: Prove/show/verify for $n=1$. Induction hypothesis: assume true for $n=k$. Step 3: Prove true for $n=k+1$. – paw88789 Aug 26 '14 at 23:13