Chapter 8: Infinite Sequences and Series
Section 8.5: Taylor Series
Obtain the Maclaurin series for 1−x21+x2 from appropriate geometric series.
Write 1−x21+x2 as 11+x2−x21+x2 and note that, by the sum formula for the geometric series, 11+x2=∑n=0∞−x2n. Thus,
11+x2−x21+x2=∑n=0∞−x2n−x2 ∑n=0∞−x2n=1−2⁢x2+2⁢x4−2⁢x6+2⁢x8−2 x10+⋯
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