By induction method, find the value of
`1*1!+2*2!+3*3!+ . . .+n*n!`.

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

Find the value of n , if (2n - 1)/(n - 2) = 3

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.1! +2.2! +3.3! +.......+ n.n! = (n+1)!-1 .

Prove the following by the method of induction for all n in N : 1.2 + 2.3 + 3.4 +...+ n(n + 1) = n/3 (n+1)(n+2).

Find the value of 2^(n){1.3.5.....(2n-3)(2n-1)}

Prove the following by the method of induction for all n in N : 1^3 + 3^3 + 5^3 + ... to n terms = n^2 (2n^2 - 1) .

Prove the following by the method of induction for all n in N : 1^2 + 2^2 + 3^2 + ... + n^2 = (n(n + 1) (2n + 1)) / 6 .

Prove the following by the method of induction for all n in N : 1.3 + 3.5 + 5.7 +... to n terms =n/3 (4n^2 + 6n - 1) .

By the principle of mathematical induction, prove that, for nge1 1^(3) + 2^(3) + 3^(3) + . . .+ n^(3)=((n(n+1))/(2))^(2)

Find the value of : m^3-1/n^3 , if m-1/n=13/2 and m/n=7/2 .