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Find a power series representation for the function and determine the interval of convergence.

$ f(x) = \frac {4}{2x + 3} $

$\frac{4}{3} \sum_{n=0}^{\infty}(-1)^{n} (\frac{2}{3})^ {n} x^{n}$

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Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

Okay, So find the powers there's representation function and determine the interval convergence. So first, we're going to rewrite this form into 4/3. We just factor of three and one plus two x over three, and this is 4th, 3rd or one times One hour, one minus next to two x over three and wake him. Expand this part. This is very familiar to us. And this will be from zero symphony minus one to the power in two thirds to the power of N and X to the power of end. And the interval of convergence is going to be so. This value is less than one, and that implies the absolute value of X is less than three or two.

University of Illinois at Urbana-Champaign