[" how by induction method that "],[qquad 1^(2)+2^(2)+3^(2)+...+n^(2)>(n^(3))/(3)quad AA n in N]

By the principle of mathematic induction, prove that, for n ge 1 , 1^(2) + 2^(2) + 3^(2) + …+n^(2) gt n^(3)/3

Use mathematical induction to prove that statement 1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N

Prove by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)

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 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 .

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

Using the principle of mathematical induction prove that : the 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 prove that 1^2+3^2+5^2+.....+(2n-1)^2=(n(2n-1)(2n+1))/3 for all n in N

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