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Prove by the principle of mathematical induction that `n<2^n"for all"n in Ndot`

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RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3,n in N

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  2. A sequence x0, x1,x2,x3, ddot is defined by lettingx0=5 and xk=4+x(k-1...

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  3. Prove by the principle of mathematical induction that n<2^n"for all"n ...

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  4. Prove by the principle of mathematical induction that for all n in N ...

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

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  6. Prove the following by using the principle of mathematical inductio...

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  7. Prove that: (1+1/1)(1+1/2)(1+1/3)(1+1/n)=(n+1) for all n in Ndot

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  8. Using principle of MI prove that 2.7^n+3.5^n-5 is divisible by 24

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  9. Prove by the principle of mathematical induction that (n^5)/5+(n^3)/3+...

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  10. For all positive integer n , prove that (n^7)/7+(n^5)/5+2/3n^3-n/(105)...

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  11. If P(n) is the statement "2^(3n)-1 . Is an integral multiple 7", and i...

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  12. Let P(n) be the statement "3^n > n" . If P(n) is true, P(n+1) is also ...

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  13. If P(n) is the statement n^2&gt; 100" , prove that whenever P(r) is...

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  14. Prove by the principle of mathematical induction that for all n in N ...

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  15. Prove by the principle of mathematical induction that for all n in N ...

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  16. Prove by the principle of mathematical induction that: n(n+1)(2n+1) is...

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  17. Prove by the principle of mathematical induction that for all n in N ...

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  18. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

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  19. Prove that 1/(n+1)+1/(n+2)+...+1/(2n)> 13/24 ,for all natural number ...

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  20. Prove the following by using the principle of mathematical inductio...

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