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Hello all,

Again I find myself at odds with my online class. Somehow, and with two problems in a row, I am finding the reciprocal answer to what Math Lab is telling me.

I would be very appreciative is someone could check my work.

Find the limit of convergence, and the radius.

\(\displaystyle \sum \frac{k^2x^{2k}}{k!}\)

Using the ratio test

\(\displaystyle \lim_{k\rightarrow \infty}\frac{(k+1)^2x^{2k+2}}{(k+1)k!}*\frac{k!}{k^2x^{2k}}\)

That should be an absolute value, but I don't know how to input that...

This should simplify down to,

\(\displaystyle x^2\lim_{k\rightarrow \infty}\frac{k^2+2k+1}{k^3+k^2}\) (with absolute values inputed)

Which should give an interval of convergence of,

\(\displaystyle 0<x^2<0\), R=0, [0,0]

My online class is showing R=\(\displaystyle \infty\) (\(\displaystyle -\infty,\infty\))

The last question gave an R=4, and I was showing R=1/4. I am reversing this somehow. Any help is appreciated.

Thanks,

Mac

Again I find myself at odds with my online class. Somehow, and with two problems in a row, I am finding the reciprocal answer to what Math Lab is telling me.

I would be very appreciative is someone could check my work.

Find the limit of convergence, and the radius.

\(\displaystyle \sum \frac{k^2x^{2k}}{k!}\)

Using the ratio test

\(\displaystyle \lim_{k\rightarrow \infty}\frac{(k+1)^2x^{2k+2}}{(k+1)k!}*\frac{k!}{k^2x^{2k}}\)

That should be an absolute value, but I don't know how to input that...

This should simplify down to,

\(\displaystyle x^2\lim_{k\rightarrow \infty}\frac{k^2+2k+1}{k^3+k^2}\) (with absolute values inputed)

Which should give an interval of convergence of,

\(\displaystyle 0<x^2<0\), R=0, [0,0]

My online class is showing R=\(\displaystyle \infty\) (\(\displaystyle -\infty,\infty\))

The last question gave an R=4, and I was showing R=1/4. I am reversing this somehow. Any help is appreciated.

Thanks,

Mac

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