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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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MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. For all nge1, prove that 1+1/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....

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

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  4. For all nge1, prove that p(n):n(n+1)(n+5) is divisible by 3.

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  5. For all nge1, prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

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  6. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

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  7. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

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  8. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Show th...

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  9. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Using t...

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  10. Consider the statement ''7^n-3^n is divisible by 4'' Verify the resu...

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  11. Consider the statement ''7^n-3^n is divisible by 4'' Prove the state...

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  12. Which among the following is the least number that will divide 7^(2n)-...

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  13. Prove by mathematical induction. (costheta +i sintheta)^n=(cosntheta...

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  14. Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true...

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  15. Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P...

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  16. Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true f...

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  17. Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the prin...

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  18. By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(...

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  19. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify t...

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  20. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assum...

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