[" S1) Prove that "1+2+3+.........],[+n=(n(n+1))/(2)," where "n in N" ."]

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

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

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

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

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

Let A=[(-1,-4),(1,3)] , by Mathematical Induction prove that : A^(n)[(1-2n,-4n),(n,1+2n)] , where n in N .

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .