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Problem 12 Medium Difficulty

Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.
$ f(x) = \frac {2x + 3}{x^2 + 3x + 2} $

Answer

$$f(x)=\sum_{n=0}^{\infty}(-1)^{n}\left[1+\left(\frac{1}{2}\right)^{n+1}\right] \cdot x^{n}$$
Radius of convergence is 1

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Video Transcript

okay. So expressive function as a sum of power, serious by first using partial fractions and find the in the role of convergence. So that bag's equals to ask for three times. So we're going to fetter out this part, It becomes at plus one times. This was too one over it. And this is just so it's a difference of two factions when investment plus one minus one or restless too. Yeah, and, ah, we can expand this part from that firm. And it just not wanted power in extra power and from zero to infinity minus. So actually, we're here. We're gonna hold out to here. So becomes one of us. Have bags end. This is just what happy soul here, minus one two hour in extra oven, over to help it. And from zero to infinity. I know him. I might as well just But it's who inside it. So this is to empower us one, and yeah, this is help. Our serious and Phil can simplify it. Bye. Plus tax insurance, the's some, but okay, we can wield it as an alternative form. So this is the same one. But if you want to know that we can destroy it. Extroverted plus one minus. If you're dating like you want our end acts to power. Plus one answered about this one. So this is the to ask past this part which is right here a parenthesis here. And the three comes this part. Here, have this that you want a part in that of an over tubes of this one. Done and find the interval burdens so we can fund it from here. Think, Creon one. So s the absolutely fattest, less than one end two over axe. That's over to the absolutely the absolute Oh, that's over, too. Is less than one wishing kleiss the interval convergence I because a two one, two, one. Okay.

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