How do you find taylor polynomials of degree n approximating $5/(2-2x)$ for x near 0?

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Answer 1 · 2016-07-28T11:43:46

$5/(2-2x) = sum_(n=0)^oo 5/2x^n$

If $abs(x) < 1$ then:

$1/(1-x) = sum_(n=0)^oo x^n$

Hence:

$5/(2-2x) = 5/(2(1-x)) = 5/2*1/(1-x) = 5/2 sum_(n=0)^oo x^n = sum_(n=0)^oo 5/2x^n$

How do you find taylor polynomials of degree n approximating 5/(2-2x)5/(2-2x) for x near 0?