Constructing a Power Series using a geometric series as a base.

i am to use

to find a power series representation for

additionally I need to find the interval of convergence.

since,

and



then




the book says is a power series representation of the original function can someone point out my error?

is correct, but it is not in the form .

we'll i don't think i can use the distributive property to make it

since this is basically an polynomial of infinitely many terms being multiplied by a binomial.

i don't really see anything to do here.

i don't know of a way to dump out the parentheses and make a " "

Quote:

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Originally Posted by bkbowser

we'll i don't think i can use the distributive property to make it

since this is basically an polynomial of infinitely many terms being multiplied by a binomial.

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This depends on the level of rigor with which you need to "find" the series for . Do you need an accurate proof that it converges to the function inside the interval of convergence? I agree that infinite sums require special care, but using distributivity in the way you did is fine as the first approximation.