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Math Help - Show by mathematical induction:

  1. #16
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    Of course Thanks!
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  2. #17
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    Quote Originally Posted by jenkki View Post
    Yes Don't know how to write sub/sup text...
    I don't think induction is necessary. To show that this is always positive, show that the numerator and denominator are always the same sign (I can't see any reason why either of them would ever be negative...)

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  3. #18
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    No, it's not necessary.
    However, the objective is to learn and practice the technique of Proof By Induction.
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  4. #19
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    Quote Originally Posted by Prove It View Post
    I don't think induction is necessary. To show that this is always positive, show that the numerator and denominator are always the same sign (I can't see any reason why either of them would ever be negative...)
    ??The denominator is just 2a_n. Saying that "I can't see any reason why either of them would ever be negative" is exactly the same as saying "I can't see any reason why a_n wouldn't be positive"- and that does NOT constitute a proof that it is!

    Indeed, since the numerator, a_n^2+ 2 is obviously always positive, saying "show that the numerator and denominator are always the same sign" is exactly the same as saying "show that a_n is always positive" which is exactly what the original problem says!
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