Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.1 Sequences - 12.1 Assess Your Understanding - Page 807: 61

$\sum_{k=1}^{13} (\frac{k}{k+1})$

We can see that this is the sum of the $13$ fractions in which the first denominator is $1$, increases by $1$ in each term and in which the first numerator is $2$, increases by $1$ in each term. Hence the summation formula is: $\sum_{k=1}^{13} (\frac{k}{k+1})$