- #1

aydin

## Homework Statement

find the radius of convergence and interval of convergence of the series

∞

Σ (3x-2)^2 / n 3^n

n=1

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- Thread starter aydin
- Start date

- #1

aydin

find the radius of convergence and interval of convergence of the series

∞

Σ (3x-2)^2 / n 3^n

n=1

- #2

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- #3

HallsofIvy

Science Advisor

Homework Helper

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is, I think, what you want.

Ratio test is probably best.

[tex]a_n= \frac{|3x-2|^n}{n n!}[/tex]

and

[tex]a_{n+1}= \frac{|3x-2|^{n+1}}{(n+1) (n+1)!}[/tex]

so the ratio is

[tex]\frac{|3x-2|^{n+1}}{(n+1)(n+1)!}\frac{n n!}{|3x-2|^n}= |3x-2|\frac{n}{(n+1)^2}[/tex]

What is the limit of that as n goes to infinity? If that is less than 1, the series will converge.

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