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Prove the following by using the principle of mathematical induction for all `n in N` :- `(2n+7) < (n + 3)^2.`

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Prove the following by using the principle of mathematical induction for all n in N :- 10^(2n-1) + 1 is divisible by 11.

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Prove the following by using the principle of mathematical induction for all n in N :- x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N :- 3^(2n+2)-8n -9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N :- 1 +2 + 3 +...+n < 1/8(2n+1)^2 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.2.3 + 2.3.4 +...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 .

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MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Prove by Induction, for all n in N : 2^n >n.

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  2. Prove by Induction, for all n in N : 2^n < 3^n.

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

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  4. Prove by Induction, for all n in N : (n+3)^2 le 2^(n+3).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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