Question

The following function can be expressed as the sum of two series, one of them is: x2 – 3x + 2 (A) Š(21)" n=0 (B)

Answer 1

First the function is written in another form using partial fraction. Then using Binomial series, the power series representation is obtained. Option B is correct. All other options are incorrect.

1. is re Geven function f(n) = - 2 x²_3472 c - x(22)-1(72) x²20-142 = 234-1) Let in zaka-17 = one + = A(+1) +B1%-2) (x-2)(art) → x = (A+B)2+(-A-28) Equating the coefficients of like powers 2B= 0 & of x A+B=6 - 2B +B=1 A=-2B) => (A=2) (B= -1) is flu) = a + Á = 2(x-25- _ (*) -2°/1-4° +(1-830 ising Bellonial o serius NIX --(-)" + (1-x)" (using Beliomie =- [ 1+*+(!)+6+--] + [1-7272*?__? thai Thus one of the series is - 2 (12) Hence oftion ® is correct. All other options ④ @ 0 . ① are incorrect