Solution Found!
Differentiating and integrating power series Find the
Chapter 8, Problem 33E(choose chapter or problem)
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.
\(g(x)=\frac{1}{(1-x)^{2}}\) using \(f(x)=\frac{1}{1-x}\)
Questions & Answers
QUESTION:
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.
\(g(x)=\frac{1}{(1-x)^{2}}\) using \(f(x)=\frac{1}{1-x}\)
ANSWER:Solution 33E
Step 1:
In this problem we need to find the power series representation for g(x) = centered at ‘0’ by differentiating or integrating the power series for f(x) =
We already know a power series for f(x) = = for
, since , and =
Therefore , power series representation for g(x) =