Differential Equation homework help

Mivg
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Homework Statement



f(x) = \sum \frac{9^{n}}{4n} x^{2n}

n=1, \infty is on top of the summation sign.

Homework Equations



a) Use the Ratio Test to find the radius of convergence of the Power Series
b) Find f \grave{}(x) and write out the first three (non-zero) terms of the power series for f \grave{}(x)
 
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You've, erm, omitted a section of the posting template, haven't you?

3. Attempt at a solution.

Come on, this is an easy Calc II problem. A Diff Eq student should at least be able to start it.
 
I got part a no problem, but having trouble with part b.
 
Mivg said:
I got part a no problem, but having trouble with part b.
There's still no attempt at a solution...
 
Some help you guys are, thanks a bunch.
 
Sorry, apparently you've found the wrong website. You meant to post on http://www.wedoyourhomeworkforyou.com .

But if you want to continue to post here, you must abide by the rules that you explicitly agreed to before registering.

To refresh your memory:

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And hey, don't get mad at me. I don't write the rules here. Oh wait, yes I do...
 
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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