Solve the Problem $\tan ^ { - 1 } x$ , Obtain a Series For

question 361

Multiple Choice

Solve the problem.
-Using the Maclaurin series for $\tan ^ { - 1 } x$ , obtain a series for $\frac { \tan ^ { - 1 } x ^ { 2 } } { x ^ { 2 } }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 4 n } } { 2 n + 2 }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 2 n } } { 2 n + 1 }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 2 n } } { 2 n + 2 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 4 n } } { 2 n + 1 }\)

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Definitions:

Cash Flows

Cash flows denote the movement of money into and out of an enterprise, playing a crucial role in assessing its operational efficiency and financial stability.

Statement of Comprehensive Income

A financial report detailing all variations in equity over a period, excluding those changes caused by investments from and distributions to shareholders.

Self-sustaining

Capable of continuing or maintaining itself independently without external assistance.

Cash Flow from Assets

The total amount of money being transferred in and out of a company from its operational activities, investment activities, and financing activities, specifically related to its assets.