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Question
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 + x)−4
Solution
(1 + x)−4
`= 1 + (-4)x + ((-4)(-4 - 1))/(2!) x^2 + ((-4)(-4 - 1)(-4 - 2))/(3!) x^3 + ...`
`= 1 + (-4)x + ((-4)(-5))/2 x^2 + ((-4)(-5)(-6))/6 x^3 + ...`
= 1 – 4x + 10x2 – 20x3 + ....
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