wiltseliz1069 wiltseliz1069

28-12-2021
Mathematics

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Find a power series representation for the following function.

f(x)=ln(1+x). sum_(n=1)^[infinity] ((-1)**n

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babbieleo40 babbieleo40

28-12-2021

a. Recall that

For , we have

By integrating both sides, we get

If , then

so that

We can shift the index to simplify the sum slightly.

b. The power series for can be obtained simply by multiplying both sides of the series above by .

c. We have

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