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Chapter 8: Q-9E (page 434)

Question : find the power series expansionfor given the expansions for f(x) and g(x).

Short Answer

Expert verified

The required expansion is.

Step by step solution

01

Find the sum of functions

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)

Let z=n-1=n=z+1

Since index is just a dummy variable, we can replace z with n; the series g(x) thus becomes

02

conclusion

The sum therefore is given by

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