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1^2+2^2+3^3+.....+n^2=(n(n+1)(2n+1))/(6)...

`1^2+2^2+3^3+.....+n^2=(n(n+1)(2n+1))/(6)`

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

Prove the following by using the principle of mathematical induction for all n in N :- 1^2+3^2+5^2 + ...+(2n-1)^2=(n(2n-1)(2n+1))/3 .

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

By the Principle of Mathematical Induction, prove the following for all n in N : 1.2+2.2^2 +3.2^3+.....+ n.2^n= (n-1)2^(n+1)+2 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1.3+2.3^2 +3.3^3+.....+ n.3^n= ((2n-1)3^(n+1)+3)/4 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 2.3^2 + 3.3^3 +... + n.3^n =((2n-1)3^(n+1) +3)/4 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1^2+2^2+3^2+ .......... + n^2> n^3/3 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. 1^2+2^2+3^3+.....+n^2=(n(n+1)(2n+1))/(6)

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  2. Let P (n) be the statement : “P(n) : 10n + 3 is prime’’. Is P(3) true...

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  3. Let P(n) be the statement ''2^n > 1’’. Is P(1) true ?

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  4. If P(n) is the statement “n(n + 1) is even’’, then what is P(4) ?

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  5. Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statem...

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  6. Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statem...

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  7. If P(n) is the statement ‘‘n^2 > 100” prove that P(r + 1) is true when...

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  8. If P(n) is the statement ‘‘2^n ge n’’, prove that P(r +1) is true when...

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  9. Let P(n) be the statement ‘‘4^n > n’’. If P(r) is true, prove that P(r...

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

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

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

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

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

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

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

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

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

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

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

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

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