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Prove the following by the principle of mathematical induction: `\ x^(2n-1)+y^(2n-1)` is divisible by `x+y` for all `n in Ndot`

A

x

B

x+1

C

`x^2+x+1`

D

`x^2-x+1`

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise-2 Concept Applicator
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  2. Prove the following by using the principle of mathematical induction ...

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  3. If n in N , then the number (2+sqrt3)^n+(2-sqrt3)^n is

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

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  5. Show by the Principle of Mathematical induction that the sum Sn, of th...

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  6. If P(n0: 49^n+16^n+lambda is divisible by 64 for n N is true, then th...

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  7. Prove the rule of exponents (a b)^n=a^n b^nby using principle of mathe...

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  8. 1 1^(n+2)+1 2^(2n+1) is divisible by 133.

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

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  10. 4 1^n-1 4^n is a multiple of 27

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

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  12. x^(2n-1)+y^(2n-1) is divisible by x+y

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  13. When 2^301 is divided by 5, the least positive remainder is

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  14. If n is a positive integer, then 2.4^(2n+1)+3^(3n+1) is divisible by :

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  15. 5^(2n+2)-24n+25 is divisible by 576

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  16. Prove the following by the principle of mathematical induction: \ x...

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  17. If P(n0: 49^n+16^n+lambda is divisible by 64 for n N is true, then th...

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  18. If n is any odd number greater than 1, then n\ (n^2-1) is divisible b...

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  19. 1/n+1/(n+1)+1/(n+2)++1/(2n-1)=1-1/2+1/3-1/4++1/(2n-1)

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  20. Show using mathematical induciton that n!lt ((n+1)/(2))^n. Where n in ...

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