Question

Find the coefficient of x^r in the expansion of (1 – 2x + 3x² – 4x³ + …)ⁿ and if x = 1/2 and n = 1, then find the value of the expression.

Answer 1

we know that (1 + x)^-2 = 1 – 2x + 3x² – 4x³ +…+ (-1)^r (r+1)x^r+ ….. (i)

Given progression (1 – 2x + 3x² – 4x³ +…)ⁿ
(1 – 2x + 3x² – 4x³ +…)ⁿ

= {(1 + x)^-2}ⁿ  [From equation (i)]

= (1 + x)^-2n