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Math Help - Proofs Questions (Real Analysis)

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    Proofs Questions (Real Analysis)

    Thanks
    Last edited by tomatoe; March 15th 2007 at 08:55 PM.
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  2. #2
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    Quote Originally Posted by tomatoe View Post
    1) Prove that if lim n approaches infinity absolute value of "a sub n + 1" over "a sub n" = L < 1, then the lim n approach infinity of "a sub n" = 0.
    Choose L<a<1.

    Now (L-a)/2 > 0


    Thus,

    ||a_{n+1}/a_n| - L|<(L-a)/2

    (L-a)/2-L<|a_{n+1}/a_n|<(L-a)/2+L

    |a_{n+1}/a_n|<(L+a)/2<(a+a)/2=a.

    Thus,
    |a_{n+1}|<a*|a_n| for n>N

    Use that to construct a geometric sequence.
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