If , prove that C_0 + 2C_1 + 3C_2 + + (n+1)C_n = (n+2)2^n -…

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

If (1+x)n=C0+C1x+C2x2+⋯+Cnxn(1+x)^n = C_0 + C_1 x + C_2 x^2 + \dots + C_n x^n , prove that C0+2C1+3C2+⋯+(n+1)Cn=(n+2)2n−1.C_0 + 2C_1 + 3C_2 + \dots + (n+1)C_n = (n+2)2^n - 1.

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