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

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