Question : find the power series expansion for given the expansions for f(x) and g(x).
The required expansion is.
We know that the power series representation of the sum of two power series, given byis simply obtained by term-wise addition:
For the given series
In order to obtain sum we need to change the index of function g(x)
Since index is just a dummy variable, we can replace z with n; the series g(x) thus becomes
The sum therefore is given by
94% of StudySmarter users get better grades.Sign up for free