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

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)

For all ninNN , prove by principle of mathematical induction that, 1^(2)+3^(2)+5^(2)+ . . .+(2n-1)^(2)=(n)/(3)(4n^(2)-1) .

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

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

If ninNN , then by principle of mathematical induction prove that, 3^(2n+2)-8n-9 is divisible by 64.

(b)Prove by the principle of mathematical induction that 3^n>2^n.