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

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

Problem

If (1+x)n=C0+C1x+C2x2(1+x)^n = C_0 + C_1 x + C_2 x^2 +C3x3+...+Cnxn+ C_3 x^3 + ... + C_n x^n , prove that C1−2C2+3C3−...+(−1)n−1nCn=0.C_1 - 2C_2 + 3C_3 - ... + (-1)^{n-1} n C_n = 0.

Related theory

Browse the problem library