consider the power series:

Question

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628

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$\sum_{n=0}^\infty \frac{n^3 x^{2n}}{5^n}.$

Determine the radius of convergence .

Guest Nov 23, 2014

+33661

+5

Best Answer

$$\sum_{n=0}^{n=\infty}n^3z^{2n}=\frac{z(z^2+4z+1)}{(z-1)^4}$$

This has a singularity at z = 5, so I guess the radius of convergence of your expression is when x²/5 = 1 or x = ±√5

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Edit: Just noticed that Chris has answered the same question elsewhere!

Alan Nov 24, 2014

Alan · Answer 1 · 2014-11-24T08:24:29

$$\sum_{n=0}^{n=\infty}n^3z^{2n}=\frac{z(z^2+4z+1)}{(z-1)^4}$$

This has a singularity at z = 5, so I guess the radius of convergence of your expression is when x²/5 = 1 or x = ±√5

.

Edit: Just noticed that Chris has answered the same question elsewhere!