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प्रश्न
Answer the following:
State, first four terms in the expansion of `(1 - (2x)/3)^(-1/2)`
उत्तर
`(1 - (2x)/3)^(-1/2) = 1 (-1/2) ((2x)/3) + ((-(1)/2)(-(1)/2 - 1))/(2!) ((2x)/3)^2 - ((-(1)/2)(-(1)/2 - 1)(-(1)/2 - 2))/(3!) ((2x)/3)^3 + ...`
= `1 - (-1/2) ((2x)/3) + ((-(1)/2)(-(3)/2))/2 ((2x)/3)^2 - ((-(1)/2)(-(3)/2)(-(5)/2))/6 ((2x)/3)^3 + ...`
= `1 + x/3 + 3/8 xx (4x^2)/9 + 15/(8 xx 6) xx (8x^3)/27 + ...`
= `1 + x/3 + x^2/6 + (5x^3)/54 + ...`
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