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Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N` :- `1+1/((1+2))+1/((1+2+3))+...+1/((1+2+3+...n))=(2n)/((n+1))`.

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MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Prove by Induction, for all n in N : (n+3)^2 le 2^(n+3).

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  2. Prove by Induction, that (2n+7)le (n+3)^2 for all n in N. Using this, ...

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

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  4. Use method of induction, prove that : If n^3+(n+ 1)^3+(n+ 2)^3 is divi...

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  5. Using mathematical induction , show that n(n+1)(n+5) is a multiple of...

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  6. Use method of induction, prove that : n(n +1)(n +2) is divisible by 6.

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  7. Use method of induction, prove that : n^3+3n^2+5n+3 is divisible by 3...

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  8. Prove, by Induction, on the inequality (1 +x)^n ge 1 +nx for all natu...

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

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

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

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

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

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

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

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

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

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

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

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

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