If (1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + + C_n x^n

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

\text{If } (1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \dots + C_n x^n, \text{ prove that}

C_1^2 + 2C_2^2 + 3C_3^2 + \dots + nC_n^2 = \frac{(2n-1)!}{(n-1)!^2}