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Math Help - Calculus 2, Math 101 Series converging or diverging help

  1. #1
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    Calculus 2, Math 101 Series converging or diverging help

    Hey guys I need help with 3 series questions I have uploaded the pictures, I know the first one is convergent and you can compare it to 1/n^2 and take the limit but I cant simplify the limit. Then for numbers 2 and 3 I am also pretty sure they are convergent, just cant do the proof.

    Thanks a ton to anyone who can help

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    Re: Calculus 2, Math 101 Series converging or diverging help

    Quote Originally Posted by harjas9 View Post
    Hey guys I need help with 3 series questions I have uploaded the pictures, I know the first one is convergent and you can compare it to 1/n^2 and take the limit but I cant simplify the limit. Then for numbers 2 and 3 I am also pretty sure they are convergent, just cant do the proof.

    Thanks a ton to anyone who can help

    For the second, you might want to try the ratio test. For the third, note that cos(n) <= 1 for all n, so what series can you compare it to?
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    Re: Calculus 2, Math 101 Series converging or diverging help

    What is the ratio test, is that when p is greater than 1 for 1/n^p?

    3. So compare it to 1/n^1/2 ? but then they are equal so how would i determine which is greater?
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    Re: Calculus 2, Math 101 Series converging or diverging help

    Also how would I simplify the limit for number 1 if I am at: n^2/(n^(1+1/lnln(n))
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