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

Using the principle of mathematical induction prove that : 1. 3+2. 3^2+3. 3^3++n .3^n=((2n-1)3^(n+1)+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 n^(3)-7n+3 is divisible by 3, AA n in N

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

Using the principle of mathematical induction, prove that n<2^n for all n in N

Using the principle of mathematical induction, prove that 1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4) for all n in N .

Using principle of mathematical induction , prove that n^(3) - 7n +3 is divisible by 3 , for all n belongs to N .

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

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N