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Question
Answer the following:
State, first three terms in the expansion of `(5 + 4x) ^(-1/2)`
Solution
`(5 + 4x)^(-1/2) = [5(1 + (4x)/5)]^(-(1)/2)`
= `5^(-(1)/2) (1 + (4x)/5)^(-(1)/2)`
= `5^(-(1)/2)[1 + (-(1)/2)((4x)/5) + ((-(1)/2)(-(1)/2 - 1))/(2!) ((4x)/5)^2 + ...]`
= `5^(-(1)/2)[1 - (2x)/5 + (-(1)/2) (-3/2) (1/2) ((16x^2)/25) + ...]`
= `5^(-(1)/2) [1 - (2x)/5 + (6x^2)/25 + ...]`
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