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# fp2 ln(1+x) mclaurin series question watch

1. As I have marked in the attachment, the book shows that the rth term of the series is (xto the power r)/r but this means if we substitute r as 0 the term is undefined?

Is the book still right?

My second question: I can see the series is valid for x>-1 because ln (1-1) =ln 0 but how can I tell the series is valid for x<1?
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2. (Original post by thebrahmabull)
As I have marked in the attachment, the book shows that the rth term of the series is (xto the power r)/r but this means if we substitute r as 0 the term is undefined?

Is the book still right?

My second question: I can see the series is valid for x>-1 because ln (1-1) =ln 0 but how can I tell the series is valid for x<1?
The series will diverge for , but converges for .
You could do so by noting that , which you can express as the sum of a GP, and infer from there that the given series is convergent for and check as special cases.
3. (Original post by thebrahmabull)
As I have marked in the attachment, the book shows that the rth term of the series is (xto the power r)/r but this means if we substitute r as 0 the term is undefined?

Is the book still right?

My second question: I can see the series is valid for x>-1 because ln (1-1) =ln 0 but how can I tell the series is valid for x<1?
The first term is x and the next involves x^2 so the general term only applies from r=1 onwards, so r will never equal 0

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