Prove the following using mathematical induction. 1. 12 + 22 + 32 + ... + n? = n(n +1)(2n + 1) for any n eN %3D 13 + 2 + 33 + ... n°(n + 1)? 4 2. + n3 !! 1.2+2.3+3 4+... + n(n + 1) = n(n +1)(n+ 2) for any neN 3. 3 4. 2 + 22 + 23 +... + 2" = 2n*1- 2, for any n eN 5. 1+8+ 16 +... + 8(n – 1) = (2n – 1)2, for any n e N n(n +3) 1-2:3*2-3-4*3.4-5* n(n + 1)(n + 2) 4(n + 1)(n + 2)' 6. 1 for any neN ... 7. n? > 2n, for any positive integer n2 3 8. 3"- 2 2 10n, for any positive integer n 2 4 9. 4° -1 is divisible by 3 for any neN MTA BA foomouo 10. n° + 3n? + 2n is divisible by 6 for any ne N

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Q: use the Principle of Mathematical Induction to show that the given statement is true for all natural…

A: To Prove: 12+22+32+...+n2=nn+12n+16

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Q: (4 – 2æ)".

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