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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 + 2 + 3 + dot dot dot + n <1/8(2n+1)^2`.

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NAGEEN PRAKASHAN ENGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise 4
  1. Prove the following by the principle of mathematical induction:\ 7^...

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  2. Prove the following by the principle of mathematical induction: 7+7...

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

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  4. Using the principle of mathematical induction ,prove that (1+x)^ngeq(1...

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  5. Using binomial theorem, prove that 2^(3n)-7n-1 is divisible by 49 , wh...

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

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  7. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

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  8. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

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  9. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

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  10. Prove by PMI that 1.2+ 2.3+3.4+....+ n(n+1) =((n)(n+1)(n+2))/3, AA n i...

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  11. 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

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  12. Prove the following by the principle of mathematical induction: \ 1...

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  13. Prove the following by the principle of mathematical induction:1/2+...

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  14. Prove the following by the principle of mathematical induction:1/(2...

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  15. Using the principle of mathematical induction prove that 1/(1. 2. ...

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

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  17. Prove the following by using the principle of mathematical induction ...

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

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  19. Prove by using the principle of mathemtical induction: 1^3+3^3+5^2+…+...

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  20. Prove the following by the principle of mathematical induction: 1/(1...

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