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`

Prove that n^5/5 + n^3/3+(7n)/(15) is a natural number.

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

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 the principle of mathematical induction: (n^7)/7+(n^5)/5+(n^3)/3+2(n^3)/3-n/105 is a positive integer for all n in Ndot

Prove the following by the principle of mathematical induction: (n^(11))/(11)+(n^5)/5+(n^3)/3+(62)/(165)n is a positive integer for n in NNdot

Prove the following by the principle of mathematical induction: \ 7^(2n)+2^(3n-3). 3^(n-1) is divisible 25 for all n in Ndot

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

Using the principle of mathematical induction, prove that n(n+1)(n+5) is a multiple of 3 for all ninN .