Find the sum.
-$\sum _ { i = 1 } ^ { 4 } \frac { i + 1 } { i + 2 }$

Question

Quizplus · Accepted Answer

To find the sum, we calculate each term individually and then add them together:1. For $i = 1$, $\frac{i + 1}{i + 2} = \frac{2}{3}$2. For $i = 2$, $\frac{i + 1}{i + 2} = \frac{3}{4}$3. For $i = 3$, $\frac{i + 1}{i + 2} = \frac{4}{5}$4. For $i = 4$, $\frac{i + 1}{i + 2} = \frac{5}{6}$Adding these fractions together: $\frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6} = \frac{8}{12} + \frac{9}{12} + \frac{48}{60} + \frac{50}{60} = \frac{17}{12} + \frac{98}{60} = \frac{61}{20}$.

Find the Sum ∑i=14i+1i+2\sum _ { i = 1 } ^ { 4 } \frac { i + 1 } { i + 2 }∑i=14​i+2i+1​

Find the Sum $\sum _ { i = 1 } ^ { 4 } \frac { i + 1 } { i + 2 }$