1.2+2.2^(2)+3.2^(3)......+n2^(n)=(12)/(5)(6^(n)-1)

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2,2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

1.2+2.2^(2)+3.2^(3)+....+n.2^(n)=(n-1)2^(n-1)+2

1.2+2.2^(2)+3.2^(3)+....+n.2^(n)=(n-1)2^(n-1)+2

1.2+2.2^(2)+3.2^(3)dots...n.2^(n)=(n-1)2^(n+1)+2

By the Principle of Mathematical Induction, prove the following for all n in N : 1.2+2.2^2 +3.2^3+.....+ n.2^n= (n-1)2^(n+1)+2 .

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

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)