Use Power Series Operations to Find the Taylor Series at X

question 171

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $$x ^ { 3 } \cos \pi x$$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n _ { 2 } } \pi ^ { 2 n + 3 } x + 2 n + 3 } { ( 2 n + 6 ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } \pi ^ { 2 n + 3 } x ^ { 2 n + 3 } } { ( 2 n ) ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n _ { \pi } } 2 n _ { x } 2 n + 3 } { ( 2 n ) ! }\)
• D) \(\sum _ { \mathrm { n } = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \mathrm { n } ^ { 2 } } \pi ^ { 2 \mathrm { n } _ { \mathrm { x } } 2 \mathrm { n } + 3 } } { ( 2 \mathrm { n } + 6 ) ! }\)

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