Question

The coefficient of x⁹ in the expansion of (1 + x) (1 + x²) (1 + x³) ….. (1 + x¹⁰⁰) is

Answer 1

x⁹ can be formed in 8 way

i.e. x⁹ , x^{1 + 8} , x^{2 + 7} , x^{3 + 6} , x^{4 + 5} , x^{1 + 2 + 6} , x^{1 + 3 + 5} , x^{2 + 3 + 4} and coefficient in each case is 1 

⇒ Coefficient of x⁹ = 1 + 1 + 1 +  .......... + 1 = 8