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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 $n≥2$ - Prove that $5_{2n+1}+2_{2n+1}$ is divisible by 7 for any positive integer $n≥0$ - 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 $n$

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