Question

If | x | < 1, then the coefficient of xn in the expansion of (1 + x + x2 + x3 + .....)2 is

(a) n – 1

(b) n

(c) n + 1

(d) n + 2

Answer 1

Answer : (c) n+1

(1 + x + x2 + x3 + .....)2

= {(1 – x) –1)}2 = (1 – x) –2

= 1 + 2x + 3x2 + 4x3 + ..... + (n + 1)xn + .....

∴ Coefficient of xn in this expansion

= (n + 1).