Given $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 5 } }$

Essay

Given $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 5 } }$ .(a) Approximate the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 5 } }$ by using the sum of the first 4 terms.(b) Estimate the error involved in the approximation in part (a).(c) How many terms are required to ensure that the sum is accurate to within 0.001?