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Math Help - Using the ratio test to show a convergent series

  1. #1
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    Using the ratio test to show a convergent series

    I'm trying to prove

    Using the ratio test to show a convergent series-tonight.gif is convergent.


    I know I need to do the ratio test but I am lost after I do the (a_n +1) / (a_n) stage. I've watched a few vidoes on using the ratio test, but nothing in the above format, please help
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  2. #2
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    Re: Using the ratio test to show a convergent series

    Quote Originally Posted by jennybee View Post
    I'm trying to prove
    Click image for larger version. 

Name:	tonight.gif 
Views:	1 
Size:	2.0 KB 
ID:	27502 is convergent.
    I know I need to do the ratio test but I am lost after I do the (a_n +1) / (a_n) stage. I've watched a few vidoes on using the ratio test.
    \frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot  \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}
    Thanks from jennybee
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  3. #3
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    Re: Using the ratio test to show a convergent series

    Quote Originally Posted by Plato View Post
    \frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot  \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}
    Thank you. Can this cancel down before I find the limit?
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