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For all nge1, prove that 1^2+2^2+3^2+…...

For all `nge1`, prove that
`1^2+2^2+3^2+……….+n^2gtn^3/3`

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MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. For all nge1, prove that 1^2+2^2+3^2+……….+n^2gtn^3/3

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  2. For all nge1,prove that 1+2+3+……+nlt1/8(2n+1)^2

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  3. For all nge1, prove that p(n):2^(3n)-1 is divisible by 7.

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  4. For all nge1, prove that p(n):n^3+(n+1)^3+(n+2)^3 is divisible by 9.

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  5. For all nge1, prove that 1/1.2+1/2.3+1/3.4+..........+1/(n(n+1))=n/(...

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  6. For all nge1, prove that 1+1/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....

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

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

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

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

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

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

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

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

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

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

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

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

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

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