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

question 197

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?

---

Definitions:

Status Quo

The existing state or condition of affairs, often used in the context of resisting change.

Force Field Analysis

A method used to identify and evaluate the forces that support or resist a particular change or decision.

State of Change

The phase or condition that an organization or individual undergoes when transitioning from one set of circumstances to another.

Imbalance of Forces

A situation in which the driving and restraining forces affecting change are not in equilibrium, affecting the rate and success of change processes.