If | x | < 1, then the coefficient of xn in (1 + 2x + 3x2 + 4x3 + .... – InterviewSolution

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1.

If | x | < 1, then the coefficient of xn in (1 + 2x + 3x2 + 4x3 + ....)1/2 is(a) 1 (b) – n (c) n (d) n + 1

Answer»

Answer : (a) 1

(1 + 2x + 3x² + 4x³ + ....)^1/2 = [(1 – x)^–2]^1/2

= (1 – x)^–1 = 1 + x + x² + x³ + .....

⇒ coefficient of each term = 1

⇒ coefficient of xⁿ = 1.

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