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[3.2^(2)+3^(2).2^(3)+3^(3).2^(4)+..........

[3.2^(2)+3^(2).2^(3)+3^(3).2^(4)+............+3^(n).2^(n+1)=(12(6^(n)-1))/(5)],[" for all "n in N]

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Using Mathematical induction prove that 3.2^(2)+3^(2).2^(3)+3^(3).2^(4)+…………+3^(n).2^(n+1)=12/6(6^(n)-1) , for all n in N

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

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 .

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 .

1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))