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, .^(n)C_(0)+.^(n)C_(1)+.^(n)C_(2)+ . . .+.^(n)C_(n)=2^(n)(ninNN)

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

By the principle of mathematical induction prove that 1+2+3+4+…n= (n(n+1))/2

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)

Use principle of mathematical induction to prove that: 1+2+3+……….+n=(n(n+1))/2

If ninNN , then by principle of mathematical induction prove that, Prove that 2+sqrt(2+sqrt(2+sqrt(2+ . . .n" times")))lt4 , for all integers nge1 .

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

Prove that by using the principle of mathematical induction for all n in N : 1+2+3+.....+n lt (1)/(8)(2n+1)^(2)

Prove that by using the principle of mathematical induction for all n in N : 1+2+3+.....+n lt (1)/(8)(2n+1)^(2)