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Math Help - Is this alternating series divergent?

  1. #1
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    Is this alternating series divergent?

    \sum (2n+3)(-1)^n/(7n+11)

    Because it is neither decreasing, nor does it have a limit of 0?
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  2. #2
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    Quote Originally Posted by Mattpd View Post
    \sum (2n+3)(-1)^n/(7n+11)

    Because it is neither decreasing, nor does it have a limit of 0?
    see the complete explanation in this link ...

    http://www.math.ucdavis.edu/~saito/courses/21C.s09/alternatingseriestest.pdf
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  3. #3
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    Quote Originally Posted by skeeter View Post
    So it's convergent? I was told it was divergent, and I am just here to double check...

    Wouldn't you just look at everything but the (-1)^n part, and see that you have (2n+3)/(7n+11) and because the powers of n are the same, the limit will be the ratio of the terms, which is 2/7, which is not 0, therefore it can't converge?
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  4. #4
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    Quote Originally Posted by Mattpd View Post
    So it's convergent? I was told it was divergent, and I am just here to double check...

    Wouldn't you just look at everything but the (-1)^n part, and see that you have (2n+3)/(7n+11) and because the powers of n are the same, the limit will be the ratio of the terms, which is 2/7, which is not 0, therefore it can't converge?
    no ... it's divergent. did you read the article?
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  5. #5
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    Quote Originally Posted by skeeter View Post
    no ... it's divergent. did you read the article?
    I did. I guess we were taught slightly wrong, because my notes say that if it fails any test, it is automatically divergent. Thank you for checking though.
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