Binomial Expansion

Express \displaystyle \frac{1+3x^{2}}{\left(1+x\right)\left(1-x\right)^{2}} in partial fractions and prove that when the function is expanded in descending powers of x, the coefficient of x^{-n} is 2n+1 or 2n-1 according as n is odd or even.  For what values of x is the expansion valid?

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 28, p. 222)

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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