Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$$
A) $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$
B) $\frac { 6 } { 7 }$
C) $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$
D) $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$

Question

Quizplus · Accepted Answer

The sum $\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$ starts with $k=1$ and ends with $k=5$, so when $k=1$, the term is $\frac{2}{3}$, and when $k=5$, the term is $\frac{6}{7}$. Choice C correctly lists all terms from $k=1$ to $k=5$.

Write Out the Sum ∑k=15k+1k+2\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }k=1∑5​k+2k+1​

Write Out the Sum $\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$