Power Series

If x is small, prove that \ln{\left(\frac{1+x^{2}}{1-x^{2}}\right)}=2x^{2}+\frac{2}{3}x^{6} approximately.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 3b, Question 20, p. 43)

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.

Leave a Reply