First principle of mathematical induction

Prove by the principle of mathematical induction that n<2^(n) for alln in N

Using principle of mathematical induction prove that sqrt(n) =2

Prove by the principle of mathematical induction that for all n in N,3^(2n) when divided by 8, the remainder is always 1.

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

Using the principle of mathematical induction , prove that for n in N , 41^(n) - 14^(n) is a multiple of 27.

Prove by the principle of mathematical induction that for all !=psi lonN;n^(2)+n is even natural no.

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .

Prove the following by the principle of mathematical induction: 1+3+3^(2)++3^(n-1)=(3^(n)-1)/(2)

Prove the following by the principle of mathematical induction: 5^(n)-1 is divisible by 24 for all n in N.

Prove the following by the principle of mathematical induction: 3^(n)+7 is divisible by 8 for all n in N.