Use Power Series Operations to Find the Taylor Series at X

question 438

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $\mathrm { x } ^ { 4 } \tan ^ { - 1 } ( 4 \mathrm { x } )$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { 2 n + 1 } x ^ { 2 n + 4 } } { 2 n + 1 }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 4 ^ { 2 n + 1 } x ^ { 2 n + 4 } } { 2 n + 1 }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 4 ^ { 2 n + 1 } x ^ { 2 n + 5 } } { 2 n + 1 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \mathrm { n } } 4 ^ { 2 n + 1 } \mathrm { x } ^ { 2 \mathrm { n } + 5 } } { 2 \mathrm { n } + 1 }\)

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