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Manipulated Taylor Series

Calculus Level 2

Determine the Taylor series centered about \(x = 0\) for the function

\[f(x) = 2x^3\sin 4x^5.\]

\[\sum_{n = 0}^{\infty}(-1)^n \frac{4^{2n + 2} x^{10n + 8}}{(2n + 1)!}\] \[\sum_{n = 0}^{\infty}(-1)^n \frac{2^{4n + 3} x^{10n + 5}}{(2n + 1)!}\] \[\sum_{n = 0}^{\infty}(-1)^n \frac{2^{4n + 3} x^{10n + 8}}{(2n + 1)!}\] \[\sum_{n = 0}^{\infty}(-1)^n \frac{4^{2n + 2} x^{10n + 5}}{(2n + 1)!}\]

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by Andrew Ellinor

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