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Let P(n) be the statement : “the arithme...

Let P(n) be the statement : “the arithmetic mean of n and (n + 2) is the same as their geometric mean”’. Prove that P(1) is not true. Also prove that if P(n) is true, then P(n + 1) is also true. How does this contradict the principle of Induction ?

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MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Prove, by Induction, on the inequality (1 +x)^n ge 1 +nx for all natu...

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  2. Let P(n) be the statement "n^2-n+41" is prime. Prove that P(1), P(2) a...

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  3. Let P(n) be the statement : “the arithmetic mean of n and (n + 2) is t...

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  4. If n straight lines in a plane are such that no two of them are parall...

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  5. Let P (n) denote the statement : “2^n gen !". Show that P(1), P(2) an...

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  6. By using the Principle of Mathematical Induction, prove the following ...

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  7. By using the Principle of Mathematical Induction, prove the following ...

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  8. Prove the following by using the principle of mathematical induction f...

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  9. Prove the following by using the principle of mathematical induction f...

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  10. By using the Principle of Mathematical Induction, prove the following ...

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  11. By using the Principle of Mathematical Induction, prove the following...

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  12. By using the Principle of Mathematical Induction, prove the following ...

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  13. Prove, by Mathematical Induction, that for all n in N, 3^(2n)-1 is d...

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  14. 10^n+3(4^(n+2))+5 is divisible by (n in N)

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  15. Prove, by Mathematical Induction, that for all n in N, 2.7^n+3.5^n-5...

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  16. Prove, by Mathematical Induction, that for all n in N, n(n + 1) (n +...

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  17. By Mathematical Induction, prove the following : (4^n+ 15n -1) is di...

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  18. By Mathematical Induction, prove the following : 12^n +25^(n-1) is d...

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  19. Prove the following by using induction for all n in N . 11^(n+2)+12^...

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  20. For all n in N, prove that : n^2/7+n^5/5+2/3 n^2-n/105 is an integer.

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