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WZ
Numerade Educator

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Problem 32 Medium Difficulty

Use the binomial series to expand the function as a power series. State the radius of convergence.

$ \sqrt [3]{8 + x} $

Answer

$2+\frac{x}{12}+2 \sum_{n=2}^{\infty}(-1)^{n+1} \frac{2 \cdot 5 \cdot 8 \cdots(3 n-4)}{24^{n} \cdot n !} x^{n}, \quad R=8$

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Video Transcript

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