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Prove the following statement.

For $0 \leq x \leq 1$, the Taylor Series, $\displaystyle x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots$ converges to $\ln(1+x)$

Any help will be greatly appreciated! Thank you!

  • 1
    Do you know the Taylor series for $\frac{1}{x}$? How can you change that function to $\ln(1+x)$ using substitution, differentiation, integration, etc.?2012-05-12
  • 0
    Have you tried showing that the [remainder](http://en.wikipedia.org/wiki/Taylor%27s_theorem#Explicit_formulae_for_the_remainder) tends to zero?2012-05-12

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