Answer
$0+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}$
$=\frac{23}{12}$
Work Step by Step
$\sum_{i=2}^5\frac{x_i+1}{x_i+2}$
$=\frac{x_2+1}{x_2+2}+\frac{x_3+1}{x_3+2}+\frac{x_4+1}{x_4+2}+\frac{x_5+1}{x_5+2}$
$=\frac{-1+1}{-1+2}+\frac{0+1}{0+2}+\frac{1+1}{1+2}+\frac{2+1}{2+2}$
$=0+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}$
$=\boxed{\frac{23}{12}}$
