Binomial Expansion

By writing \displaystyle \frac{1}{x+2} in the form \displaystyle \frac{1}{x}\left(1+\frac{2}{x}\right)^{-1}, expand \displaystyle \frac{1}{x+2} as a series of descending powers of x.  For what values of x is the expansion valid?

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 16b, Question 19, p. 218)

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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