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प्रश्न
Simplify first three terms in the expansion of the following
`(5 + 4x)^(-1/2)`
उत्तर
`(5 + 4x)^(-1/2)`
= `[5(1 + 4/5x)]^(-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))/2 ((16x^2)/25) + ....]`
= `5^(-1/2) [ 1 - (2x)/5 + (6x^2)/25 + ......]`
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