Find the sum of the convergent series. $$\sum _ { n = 1 } ^ { \infty } \frac { 9 } { ( n + 9 ) ( n + 11 ) }$$
A) $\frac { 189 } { 220 }$
B) $\frac { 135 } { 143 }$
C) $\frac { 351 } { 220 }$
D) $\frac { 61 } { 55 }$
E) $\frac { 19 } { 20 }$

Question

Quizplus · Accepted Answer

The series can be decomposed using partial fraction decomposition, and then telescopes to give the sum $\frac{189}{220}$.

Find the Sum of the Convergent Series ∑n=1∞9(n+9)(n+11)\sum _ { n = 1 } ^ { \infty } \frac { 9 } { ( n + 9 ) ( n + 11 ) }n=1∑∞​(n+9)(n+11)9​

Find the Sum of the Convergent Series $\sum _ { n = 1 } ^ { \infty } \frac { 9 } { ( n + 9 ) ( n + 11 ) }$