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If (1 + x)n = C0 + C1x + C2 x2 + ............. + cn xn , then show that 

C0 + 3C1 + 32C2 + .......... + 3nCn = 4n.

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(1 + x)n = C0 + C1 x + C2 x2 + ........... + Cn xn 

put x = 3 

C0 + 3 . C1 + 32 . C2 + .......... + 3n . Cn = 4n

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