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Math Help - prime series......

  1. #1
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    prime series......

    I was just trying to solve the problem from a book by David M. Burton.

    If any help in formulating a solution can be rendered, I shall be highly obliged.



    thanks
    kaka
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  2. #2
    Super Member craig's Avatar
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    To repeat what I put in your last post.

    If you want people to take the time to solve your questions please make the effort to write out the question in full, and not just provide a download link.

    Thankyou
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  3. #3
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    Quote Originally Posted by craig View Post
    To repeat what I put in your last post.

    If you want people to take the time to solve your questions please make the effort to write out the question in full, and not just provide a download link.

    Thankyou

    I think providing a PDF file is fine; I, on the other hand, would never open an unknown .doc file...

    Tonio
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by kaka1988 View Post
    Let  p_n denote the  n^{th} prime. For  n>3 , show that  p_n<p_1+p_2+p_3+\ldots+p_{n-1} .
    Prove this by induction. I'll leave the base case of  n=4 to you.

    Now suppose  p_n<p_1+p_2+p_3+\ldots+p_{n-1} , then  p_n+p_n<p_1+p_2+p_3+\ldots+p_{n-1}+p_n .

    But Bertrand's Postulate tells us that  p_{n+1}<2p_n .

    So we get  p_{n+1}<2p_n<p_1+p_2+p_3+\ldots+p_n , which proves the claim.
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  5. #5
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    I apologise....

    Actually I don't know how to use [tex] tags, that's why i had to use a .doc file to post my question.

    Kindly guide me.


    thanks kaka
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  6. #6
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    Quote Originally Posted by kaka1988 View Post
    Actually I don't know how to use [tex] tags, that's why i had to use a .doc file to post my question.

    Kindly guide me.


    thanks kaka

    Read "LaTeX Help" in the section "Math Resources"

    Tonio
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