radius of convergence

determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

((1-x)^2n) / ((4^n) * n)

This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..

Quote:

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Originally Posted by calculushelptx

determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

((1-x)^2n) / ((4^n) * n)

This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..

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apply the root test. can you continue?

I applied the ratio test and got 1/4 < 1 but cannot continue with root.

Quote:

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Originally Posted by calculushelptx

I applied the ratio test and got 1/4 < 1 but cannot continue with root.

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whatever you are applying, it is not the ratio test. by the ratio test, we get

now find the range for x. and remember to check the endpoints when finished