- #1
Eric Song
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Homework Statement
What is the power series for the function ln (x+1)? How do you find the sum of an infinite power series?
Homework Equations
sigma from n=1 to infinity (-1)^n+1 (1/n2^n)
That is the power series, how is that equivalent to ln (x+1)?
How do you find the sum, or what does it converge to?
The Attempt at a Solution
I know that the series converges via the ratio test: (-1)^n+2 (1/n2^n+1)/ (-1)^n+1 (1/n2^n) < 1.
So it converges, but how do I go from the power series to the function of ln(x+1)? I tried looking at known series, but still not sure. Also, how do I find the sum?