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For all nge1, prove that 1/1.3+1/3.5+1...

For all `nge1`, prove that
`1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n/(2n+1)`

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A N EXCEL PUBLICATION-PRINCIPLE OF MATHEMATICL INDUCTION-QUESTION BANK
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  4. Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in...

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  5. Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the state...

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  6. Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is t...

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  7. Let P(n) be the statement "n+3" is prime. Is P(3) true? What is your...

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  8. Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m)...

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  9. Using mathematical induction prove that 1^3+2^3+3^3+.....+n^3=[(n(n+1)...

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  10. Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statem...

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  11. Let P(n) denotes the statement 2^n gt n and if P(n) is true, show that...

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  12. Show that x^n-1 is divisible by x-1

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  13. Let P(n) denotes the statement '3^n gt 2^n'. Is P(1) true?

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  14. By using mathematical induction prove that 1+4+7+...+(3n-2)=(n(3n-1))/...

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  15. For all nge1, prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n...

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  16. For all nge1, prove that 1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n...

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  17. Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 ...

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  18. Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 ...

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  19. Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) tru...

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  20. By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) i...

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