Provide an Appropriate Response $\tan ^ { - 1 } x = \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } x ^ { 2 n - 1 } } { ( 2 n - 1 ) }$

question 350

Multiple Choice

Provide an appropriate response.
-Use the fact that $\tan ^ { - 1 } x = \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } x ^ { 2 n - 1 } } { ( 2 n - 1 ) }$ for $| x | < 1$ to find the series for $\cot ^ { - 1 } x$ .

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

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