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Let U1 =1, U2=1 and U(n+2)=U(n+1)+Un for...

Let `U_1 =1, U_2=1` and `U_(n+2)=U_(n+1)+U_n` for `nge1`. Use Mathematical Induction to show that: `U_n= 1/sqrt5[((1+sqrt5)/2)^n-((1-sqrt5)/2)^n]` for all `n ge1`.

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MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Let P(n) be the statement : “the arithmetic mean of n and (n + 2) is t...

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  2. If n straight lines in a plane are such that no two of them are parall...

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  3. Let P (n) denote the statement : “2^n gen !". Show that P(1), P(2) an...

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  4. By using the Principle of Mathematical Induction, prove the following ...

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  5. By using the Principle of Mathematical Induction, prove the following ...

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  6. Prove the following by using the principle of mathematical induction f...

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  7. Prove the following by using the principle of mathematical induction f...

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  8. By using the Principle of Mathematical Induction, prove the following ...

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  9. By using the Principle of Mathematical Induction, prove the following...

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  10. By using the Principle of Mathematical Induction, prove the following ...

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  11. Prove, by Mathematical Induction, that for all n in N, 3^(2n)-1 is d...

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  12. 10^n+3(4^(n+2))+5 is divisible by (n in N)

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  13. Prove, by Mathematical Induction, that for all n in N, 2.7^n+3.5^n-5...

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  14. Prove, by Mathematical Induction, that for all n in N, n(n + 1) (n +...

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  15. By Mathematical Induction, prove the following : (4^n+ 15n -1) is di...

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  16. By Mathematical Induction, prove the following : 12^n +25^(n-1) is d...

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  17. Prove the following by using induction for all n in N . 11^(n+2)+12^...

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  18. For all n in N, prove that : n^2/7+n^5/5+2/3 n^2-n/105 is an integer.

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  19. Prove that : cos A cos 2A cos 2^2 A cos 2^3 A........ cos 2^(n-1) A=...

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  20. Let U1 =1, U2=1 and U(n+2)=U(n+1)+Un for nge1. Use Mathematical Induct...

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