`1.2+2.2^(2)+3.2^(2)+. . . +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

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)dots...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

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 .

Prove the following 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) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

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