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5*1*3+2*3^(2)+3*3^(3)+......+n*3^(n)=((2...

5*1*3+2*3^(2)+3*3^(3)+......+n*3^(n)=((2n-1)3^(n+1)+3)/(4)

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Using the principle of mathematical induction prove that : the 1.3+2.3^(2)+3.3^(3)++n.3^(n)=((2n-1)3^(n+1)+3)/(4) for all n in N.