If `A=[costhetaisinthetaisinthetacostheta]` , then prove by principle of mathematical induction that `A^n=[cosn\ thetaisinn\ thetaisinn\ thetacosn\ theta]` for all `n in N` .

If A=[[costheta,isintheta],[isintheta,costheta]], then prove by principal of mathematical induction that A^n=[[cosntheta, i sinn theta],[isin n theta, cos n theta]] for all n in NN .

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

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

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

Prove by the principle of Mathematical Induction that log x^(n)=nlogx , 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.

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Prove by the principle of mathematical induction that: n(n+1)(2n+1) is divisible by 6 for all n in Ndot

Prove by the principle of mathematical induction that (n^5)/5+(n^3)/3+(7n)/(15) is a natural number for all n in Ndot