Consider the Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 1 } { n ^ { 4 } }$

question 26

Essay

Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 1 } { n ^ { 4 } }$ .(a) Show that the series is absolutely convergent.(b) How many terms of the series do we need to add in order to find the sum to within 0.001?
(c) What is the approximation sum in part (b)?

Understand the relationship between dividend payout ratios and additions to retained earnings.

Determine the required increase in fixed assets due to projected sales increases.

Calculate the external financing needed (EFN) based on sales projections and financing conditions.

Understand the impact of sales capacity on full-capacity sales levels.

---

Definitions:

Memory

The capability of the mind to retain and recall information.

Lincoln Penny

A one-cent coin currently minted in the United States, bearing the image of President Abraham Lincoln.

Encoding Failure

A cause of forgetting that occurs when information was never put into long-term memory.

Anterograde Amnesia

A condition in which the ability to create new memories after the event that caused the amnesia is lost, leaving the past memories intact.