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# Find a power series representation for $f,$ and graph $f$ and several partial sums $s_n(x)$ on the same screen. What happens as $n$ increases?$f(x) = \ln \left( \frac {1 + x}{1 - x} \right)$

## $\sum_{n=0}^{\infty} \frac{2 x^{2 n+1}}{2 n+1}$

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##### Top Calculus 2 / BC Educators  ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University

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the problem is, find a power. Siri's reps of condition Oh, on the graph, half on the several partial sums as in Max on the same screen. What happens as any increases So first to behalf. Want over one last Max? Yes, he caught you some from zero to infinity. Negative acts to the part ofthe end. Then we have out in one plus X is the country's integral one over one plus x Jax. This is equal to some off from zero to twenty. Nate, you want the power and hands next to the pop off us one over and plus one plus constant number. See here accidents. Last someone absolutely a fax. It's unless someone we put ax got zero in this equation and up a time out. One plus zero is equal to C. C. Is a portal zero On behalf of Alan one last sax. It's equal to the sum of from zero to infinity. Like you want the power ofthe end times X to the power ofthe plus one over and plastic. Then how how in one minus acts is the call to some ofthe from zero to infinity makes you want the power off and you will replace Axe. I make your backs. Which is is that what you're? Some from zero to infinity next to one ham's acts to the powerful plus one over and plus what then? Off Max, If he called you out in one plus x minus. Alan one minus X This is a call to some from zero to infinity. Makes you want the power on and last one. Ham's facts to the public on plus one over plus one. This is iniquitous truth times The sum from zero to infinity Act two The part ofthe two and plus one over to hand us one. You're absolutely off. ACS is the last one. Now let's look at the graph off half a box and we can graft I Cyril a swan I us three. The partial sums a serial as one on US three not to start as any increases. As a max, the partial sums becomes a biting approximation to athletics. Oh, after a while, you off X is less somewhat

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##### Top Calculus 2 / BC Educators  ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University

Lectures

Join Bootcamp