#### Answer

$\sum_{k=1}^{10} (-1)^k(\frac{k+1}{k+4})$

#### Work Step by Step

We can see that this is the sum of the $10$ fractions in which the first numerator is $2$, increases by $1$ in each term and in which the first denominator is $5$, increases by $1$ in each term. Also, the signs are alternating, starting with $-$. Hence the summation formula is: $\sum_{k=1}^{10} (-1)^k(\frac{k+1}{k+4})$