`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

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)

1.2.3+2.3.4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

Prove, by method of induction, for all n in N : 2 + 3.2 +4.2^2 +...+ (n + 1) (2^(n-1)) = n.2^n

Prove by PMI that 1.2+2.3+3.4+....+n(n+1)=((n)(n+1)(n+2))/(3),AA n in N

1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

Prove that : 1^(2)+2^(2)+3^(2)+...+n^(2)=(n(n+1)(2n+1))/(6)

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