Power Series

Expand in powers of x as far as the term in x^{3}:

    \[\ln{\frac{1+2x}{1-2x}}-\ln{\left(\frac{1+x}{1-x}\right)^{2}}\]

For what values of x is this expansion valid?

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Chapter III Miscellaneous Examples, Question 2, p. 48)

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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