Chapter 8: Infinite Sequences and Series
Section 8.5: Taylor Series
Obtain the Maclaurin series for x/1−x2 from an appropriate geometric series.
From the formula for the sum of a geometric series with r=x, obtain 11−x=∑n=0∞xn. In the right-hand side, replace x with x2, and multiply the resulting series termwise by x. The result is then x1−x2=∑n=0∞x2 n+1. A Maple corroboration is obtained as follows.
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