SOLUTION: Please would someone help, Obtain the Maclaurin series expansion about the point 0 for the function ln(x + 1) as ln(x + 1) = x -x^2/2+x^3/3 - ...+ (-1)^n+1 x^n/n+ ...   N

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Question 380351: Please would someone help,
Obtain the Maclaurin series expansion about the point 0 for the function ln(x + 1) as
ln(x + 1) = x -x^2/2+x^3/3 - ...+ (-1)^n+1 x^n/n+ ... 

Note that we cannot find a Maclaurin expansion of the function ln x since ln x does not exist at x = 0 and so cannot be differentiated at x = 0.

Thanks in advance
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
This is equivalent to finding the power series of ln x centered around x = 1. Note that all derivatives of ln x at x = 1 are equal to 1 or -1. Since we have the power series
ln+%28x%29+=+%28x-1%29+-+%28%28x-1%29%5E2%29%2F2+%2B+%28%28x-1%29%5E3%29%2F3+-+...
Adding one to all the x terms produces the given result.