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If P(n) is the statement “sum of first n...

If P(n) is the statement “sum of first n natural numbers is divisible by n + 1", prove that P(r + 1) is true if P(r) is true.

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MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Let P(n) be the statement ‘‘4^n > n’’. If P(r) is true, prove that P(r...

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  2. If P(n) is the statement ''2^(3n)-1 is an integral multiple of 7", pro...

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  3. If P(n) is the statement “sum of first n natural numbers is divisible ...

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  4. Give an example of a statement P(n), which is true for all n ge 4, but...

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  5. Give an example of the following statement : P(n) such that it is true...

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  6. Give an example of the following statement : P(n) such that P(3) is tr...

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  7. If P(n) is the statement : ''^nCr len ! for 1 le r len ", then : find ...

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  8. If P(n) is the statement : ''^nCr len ! for 1 le r len ", then : show ...

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  9. Prove that the Principle of Mathematical Induction does not apply to t...

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  10. Prove that the Principle of Mathematical Induction does not apply to t...

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  11. By the Principle of Mathematical Induction, prove the following for al...

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  12. By the Principle of Mathematical Induction, prove the following for al...

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  13. By the Principle of Mathematical Induction, prove the following for al...

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  14. By the Principle of Mathematical Induction, prove the following for al...

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  15. By the Principle of Mathematical Induction, prove the following for al...

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

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  17. By the Principle of Mathematical Induction, prove the following for al...

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

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

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  20. By the Principle of Mathematical Induction, prove the following for al...

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