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Math Help - Proof Question

  1. #1
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    Proof Question

    How would I prove that for any a > 1,

    1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
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  2. #2
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    Quote Originally Posted by thamathkid1729 View Post
    How would I prove that for any a > 1,

    1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
    Observer that for a>1:

    \dfrac{1}{a+1}\ge \dfrac{1}{a+n}

    where $$ n is a positive integer
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  3. #3
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    Quote Originally Posted by thamathkid1729 View Post
    How would I prove that for any a > 1,

    1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
    \displaystyle{\frac{1}{a+1}+\frac{1}{a+2}+\ldots +\frac{1}{a^2}\geq \frac{a^2-a}{a^2}}

    Tonio
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  4. #4
    MSM
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    Found a solution

    E=1/(a+1)+1/(a+2)...1/a^2
    E>N/(a+1)
    N=a^2-a
    E>(a^2-a)/(a+1)>(a^2-a)/a^2
    I want a real challenge
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