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Math Help - Infinite Series (15).

  1. #1
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    Infinite Series (15).

    Hello
    two hard problems:
    1) Find a series \sum a_n involves factorial but the ratio test can not determine its convergence, i.e. \lim_{n\to\infty} \frac{a_{n+1}}{a_n}=1
    2) Use only the comparison test to show that \sum_{n=1}^{\infty} \frac{1}{n!} converges provided that the series (which you will use in the comparison) satisfy the conditions of the integral test and its nth term is integrable.

    Actually I tried many times.
    but they are too hard to me

    and this is not for my homework
    Actually, we do not have homeworks in my college
    and sorry for my bad english
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For 2

    1/n! < 1/n^2 n> 4
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  3. #3
    MHF Contributor
    Jester's Avatar
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    How about  <br />
\sum_{n=1}^{\infty} \frac{n!}{n!+1}<br />
for the first.
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  4. #4
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    Quote Originally Posted by Danny View Post
    How about  <br />
\sum_{n=1}^{\infty} \frac{n!}{n!+1}<br />
for the first.
    Thanks
    But it must have "one" factorial
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  5. #5
    Math Engineering Student
    Krizalid's Avatar
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    but you got the idea!
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  6. #6
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    Quote Originally Posted by Krizalid View Post
    but you got the idea!
    No. It didn't.
    I still can not catch it.

    Sorry for my bad english
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  7. #7
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    Any one ??
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