Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 50

$3+5+7+9+...+(2n+1) $

We see that there are $n$ terms, as the index $k$ changes from $1$ to $n$. The index $k$ indicates how the terms are formed. We write out the sum for the terms as follows: $\displaystyle \sum_{k=1}^{n} (2k+1) = (2(1)+1)+(2(2)+1)+(2(3)+1)+...+(2n+1) \\=3+5+7+9+.. .+(2n+1) $