If , prove that…

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

Problem

If (1+x)n=C0+C1x+C2x2+⋯+Cnxn(1+x)^n = C_0 + C_1x + C_2x^2 + \dots + C_n x^n , prove that C0+3C1+5C2+⋯+(2n+1)Cn=(n+1)2nC_0 + 3C_1 + 5C_2 + \dots + (2n+1)C_n = (n+1)2^n .

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