Using mathematical induction, prove the following: `1+2+3+...+n< (2n+1)^2 AA n in N`

By the principle of mathematical induction prove that the following statement are true for all natural numbers 'n' n (n+1) (n+5) is a multiple of 3.

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

Using mathematical induction, to prove that 1*1!+2*2!+3.3!+ . . . .+n*n! =(n+1)!-1 , for all n in N

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .

Using mathematical induction , to prove that 7^(2n)+2^(3n-3). 3^(n-1) is divisible by 25 , for al n in N

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

Using principle of mathematical induction prove that sqrtn = 2 .

Using principle of mathematical induction prove that sqrtn = 2 .

Using principle of mathematical induction prove that sqrtn = 2 .