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).