Power Series

If x is small, prove that \displaystyle \frac{1}{1+x}-e^{-x}=\frac{1}{2}x^{2}-\frac{5}{6}x^{3} approximately.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 3a, Question 7, p. 39)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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