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# Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.$f(x) = \frac {2x - 4}{x^2 - 4x + 3}$

## $(2 -x)\left(\frac{1}{3} \sum_{n=0}^{\infty} \frac{x^{n}}{3^{n}}+\sum_{n=0}^{\infty} x^{n}\right)$interval: (-1,1)

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Okay, So expect function as the some power Siri's first using partial corrections and find the interval convergence. Okay, so everyone x as two times X minus two. And the denominator is that's minus one times. It's my three. Okay? And this is just and that's money. Three. The inverse of that's my three minus one over X minus. What? So inside here, it's always this part. So this difference equals two X minus three times X minus one and the Obama's gonna be accidents one minus X men three. So this is to actually yes. So we have this equipments. Okay, So you continue doing this is going to transform too, which is pull out three. And the inside is gonna be a sword. Three months, one and manager minus X minus wesser. This is plus one over one month's X. And here is which is pull out next one. So, uh, this turns to be two months sex, and here it goes to one minus has all three. Yet and so this part, this kind should be so it is expand, then turn by term silly, becomes extra power inthe rated out and inform zero to in a Plus, that's power in from zero to infinity. So that is thie. Some of power, Siri's. And what is Thie? Inderal of convergence. So we require Iris. That's over three is less than one. The absolute alibis, Authoress. That's what ended the actual axe. Is this one. So that that becomes silly, actually. Well, if X is less than three and someone so Leslie Thean, welcome earns is gonna be once want to what?

University of Illinois at Urbana-Champaign

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