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Question
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 + x2)–1
Solution
(1 + x2)–1
= `1 + (-1)x^2 + ((-1)(-1 - 1))/(2!)(x^2)^2 + ((-1)(-1 -1)(-1 - 2))/(3!) (x^2)^3 + ...`
= `1 - x^2 + ((-1)(-2))/2 x^4 + ((-1)(-2)(-3))/6 x^6 + ...`
= 1 – x2 + x4 – x6 + ...
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