Find the $n ^ { \text {th } }$ partial sum $S _ { n }$ of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum. $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { n + 10 } - \frac { 1 } { n + 8 } \right)$

Question

Quizplus · Accepted Answer

The Answer of Find the $n ^ { \text {th } }$ partial sum $S _ { n }$ of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum. $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { n + 10 } - \frac { 1 } { n + 8 } \right)$

Find The nth n ^ { \text {th } }nth Partial Sum SnS _ { n }Sn​

Find The $n ^ { \text {th } }$ Partial Sum $S _ { n }$