If `ninNN`, then by princuple of mathematical induction prove that,
`(1)/(5)n^(5)+(1)/(3)n^(3)+(1)/(15)*7n` is an integer.

If ninNN , then by princuple of mathematical induction prove that, (n^(11))/(11)+(n^(5))/(5)+(n^(3))/(3)+(62n)/(165) is an integer.

If ninNN , then by principle of mathematical induction prove that, 1+2+3+....+nlt(1)/(8)(2n+1)^(2) .

If ninNN , then by principle of mathematical induction prove that, 1^(2)+2^(2)+3^(2)+....+n^(2)gt(n^(3))/(3) .

By mathematical induction prove that, (n^(7))/(7)+(n^(5))/(5)+(2n^(3))/(3)-(n)/(105) is an integer for all ninNN .

If ninNN , then by principle of mathematical induction prove that, 10^(n)+3*4^(n+2)+5" "[nge0] is divisible by 9.

If ninNN , then by principle of mathematical induction prove that, 3^(4n+1)+2^(2n+2)" "[nge0] is a multiple of 7.

If ninNN , then by principle of mathematical induction prove that, 5^(2n+2)-24n-25 is divisible by 576.

If ninNN , then by princuple of mathematical induction prove that, n*1+(n-1)*2+(n-2)*3+ . . . +2*(n-1)+1*n=(1)/(6)n(n+1)(n+2)

If ninNN , then by principle of mathematical induction prove that, .^(n)C_(0)+.^(n)C_(1)+.^(n)C_(2)+ . . .+.^(n)C_(n)=2^(n)(ninNN)

By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(n-1)=(5^n-1)/4