Prove by the principle of mathematical induction that for all `n in N :` `1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)`

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

Prove by the principle of mathematical induction that 2^ n >n for all n∈N.

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by the principal of mathematcal induction that for all n in N . 1^(2) + 3^(2) + 5^(2) + …… + (2n - 1)^(2) = (n(2n - 1) (2n + 1))/(3)

Using the principle of mathematical induction, prove that n<2^n for all n in N

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove the following by using the principle of mathematical induction for all n in N : 1^2+3^2+5^2+dotdotdot+(2n-1)^2=(n(2n-1)(2n+1))/3

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

Prove by the principle of mathematical induction that for all n belongs to N :\ 1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)