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Question
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 – x2)–3
Solution
(1 – x2)–3
= `1 - (- 3)x^2 + ((-3)(-3 - 1))/(2!) (x^2)^2 - ((-3)(-3 - 1)(-3 - 2))/(3!) (x^2)^3 + ...`
= `1 + 3x^2 + ((-3)(-4))/2 x^4 - ((-3)(-4)(-5))/6 x^6 + ...`
= 1 + 3x2 + 6x4 + 10x6 + ...
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