Find the sum of the sequence.
-$$\sum _ { k = 5 } ^ { 8 } \frac { 1 } { k + 4 }$$
A) $- \frac { 197 } { 210 }$
B) $\frac { 624 } { 625 }$
C) 42
D) $\frac { 763 } { 1980 }$

Question

Quizplus · Accepted Answer

The given sequence is $\sum _ { k = 5 } ^ { 8 } \frac { 1 } { k + 4 }$. To find the sum, substitute the values of $k$ from 5 to 8 into the formula and add the results:For $k = 5$, the term is $\frac{1}{5+4} = \frac{1}{9}$.For $k = 6$, the term is $\frac{1}{6+4} = \frac{1}{10}$.For $k = 7$, the term is $\frac{1}{7+4} = \frac{1}{11}$.For $k = 8$, the term is $\frac{1}{8+4} = \frac{1}{12}$.Adding these terms together gives $\frac{1}{9} + \frac{1}{10} + \frac{1}{11} + \frac{1}{12}$.This simplifies to $\frac{763}{1980}$, which matches option D.

Find the Sum of the Sequence ∑k=581k+4\sum _ { k = 5 } ^ { 8 } \frac { 1 } { k + 4 }k=5∑8​k+41​

Find the Sum of the Sequence $\sum _ { k = 5 } ^ { 8 } \frac { 1 } { k + 4 }$