(Solved): Extra Credit 1. Use mathematical induction to solve any 3 out of the following 5 problems. - Show t ...

Extra Credit 1. Use mathematical induction to solve any 3 out of the following 5 problems. - Show that $n^5-n$ is divisible by 5 for any positive integer $n\ge 2$ - Prove that $5^{2n+1}+2^{2n+1}$ is divisible by 7 for any positive integer $n\ge 0$ - Show that $n^4-1$ is divisible by 16 for all odd integers $n$ - Prove that $n^3+2n$ is divisible by 3 for all integers $n$ - Prove that $2^n+1$ is divisible by 3 for all odd integers $n$