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anonymous

  • 5 years ago

Let \[a_{1}, a _{2}......\] be a Fibonacci series. I have a book which has a problem under the "mathematical induction" chapter, which asks me to prove \[a _{n+1}^{2}=a _{n}a _{n+2}=(-1)^{n}\] I think the statement is incorrect. For n=1, we don't have the statement correct, and I can't expect it to be correct for n>1 as \[(-1)^{n}\] will always only have values either +1 or -1, and the expression \[a _{n}a _{n+2}\] will have increasing value. Do you think I am correct, or is there really a prove for the statement. Please provide me some help.

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  1. anonymous
    • 5 years ago
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    \[a_{n+2}a_n-a_{n+1}^2=(-)^n\]is a true statement.

  2. anonymous
    • 5 years ago
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    But the statement given there is not correct, am I right?

  3. anonymous
    • 5 years ago
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    So your '=' sign is not a typo.?

  4. anonymous
    • 5 years ago
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    No

  5. anonymous
    • 5 years ago
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    When then it's incorrect.

  6. anonymous
    • 5 years ago
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    It should be a minus sign.

  7. anonymous
    • 5 years ago
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    Thanks A LOT

  8. anonymous
    • 5 years ago
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    np

  9. anonymous
    • 5 years ago
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    I told you a genius like you will need a look to solve the problem

  10. anonymous
    • 5 years ago
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    You don't have any idea, what help you are providing just free of cost

  11. anonymous
    • 5 years ago
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    Anyways, You are a busy person, so I must not hold you here, Bye

  12. anonymous
    • 5 years ago
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    :) I haven't had a chance to look at the other question yet. I'm thinking the problem can be solved by proving first that linking the last contestant to fight the one left over at the beginning is the same as linking the new (k+1) guy to somewhere else in the system. Once that's done, the induction is as we said.

  13. anonymous
    • 5 years ago
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    That sounds awkward.

  14. anonymous
    • 5 years ago
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    I should have more time in the middle of the week. When is STEP?

  15. anonymous
    • 5 years ago
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    20th June 2011 PM STEP Paper II takes place 22nd June 2011 PM STEP Paper III takes place 24th June 2011 AM STEP Paper I takes place

  16. anonymous
    • 5 years ago
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    ok...plenty of time!

  17. anonymous
    • 5 years ago
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    Yes thats true

  18. anonymous
    • 5 years ago
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    Alright, I have to go do some work. Like I said, middle of the week will be better.

  19. anonymous
    • 5 years ago
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    But I am taking several other similar exams, which you haven't heard of

  20. anonymous
    • 5 years ago
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    Sure bye now

  21. anonymous
    • 5 years ago
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    What are you intending to do with the results of the exams?

  22. anonymous
    • 5 years ago
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    I will email that to you. People will not like me saying such things here. They will think i am too presumptuous

  23. anonymous
    • 5 years ago
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    ok

  24. anonymous
    • 5 years ago
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    i'm off now. happy studies.

  25. anonymous
    • 5 years ago
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    Thanks and bye

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