If , prove that 3C_0 + 3^2 C_1 2 + 3^3 C_2 3 + + 3^n C_n n+1 = 3^ n+1 C_0 4^ n+1…

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

Problem

If

(1+x)^n = C_0 + C_1 x + C_2 x^2 + \dots + C_n x^n

, prove that

3C_0 + 3^2 \frac{C_1}{2} + 3^3 \frac{C_2}{3} + \dots + \frac{3^n C_n}{n+1} = \frac{3^{n+1} C_0}{4^{n+1}-1}

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