Geometric/binomial series Recall that the Taylor series

Chapter 8, Problem 64E

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QUESTION:

Geometric/binomial series Recall that the Taylor series for f(x) = 1/(1 - x) about 0 is the geometric series \(\sum_{k=0}^{\infty} x^{k}\). Show that this series can also be found as a case of the binomial series.

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QUESTION:

Geometric/binomial series Recall that the Taylor series for f(x) = 1/(1 - x) about 0 is the geometric series \(\sum_{k=0}^{\infty} x^{k}\). Show that this series can also be found as a case of the binomial series.

ANSWER:

Solution 64E

Step 1:

We know that the Taylor series for  about 0 is the geometric series  that is

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