" 9."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

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

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

Prove by. mathematical induction : 1.2+2.2^2+3.2^3+...+n.2^n=(n-1)2^(n+1)+2,n in N

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) = .......

1+2.2+3.2^(2)+4.2^(3)+...+n*2^(n-1) = (i) 1+ (1+n) 2^(n) (ii) 1- (1+n) 2^(n) (iii) 1- (1-n) 2^(n) (iv) 1+ (1-n) 2^(n)