Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 903: 60

$S_n=n^2$

We have to find a formula for the sum of the first n consecutive odd numbers starting with $1$: $1+3+5+ . . . +(2n-1)$ We have an arithmetic sequence with $a_1=1$, $d=2$ and $a_n=(2n-1)$ The sum $S_n=\dfrac{a_1+a_n}{2}n=\dfrac{1+2n-1}{2}n=n^2$