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Series convergent questions

  1. Dec 18, 2013 #1
    1. The problem statement, all variables and given/known data


    1. Determine if arctan(7+1/n)-arctan(7) converges or diverges

    2. Determine if 2/1-1/2-1/3+2/4-1/5/-1/6+2/7... converge or diverge

    2. Relevant equations

    series tests


    3. The attempt at a solution

    1.My gut instinct is to do limit comparison test w/ 1/n, and it worked and I got divergent, but I really don't get why.
    2. I did a similar problem in which we group every 3 terms. However, in class, the 2nd and 3rd terms were >0 and every third term combined made a divergent series, so comparision test yields divergent. But in this series, the 2nd and 3rd terms would make the series 0 to inf 2/(3n-2) smaller and it's inconclusive whether smaller than divergent is convergent or divergent.
     
  2. jcsd
  3. Dec 18, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You need to show some more of your work to get an answer. How did get a comparison with 1/n. And for the second one what's the expression for the sum of the 3 grouped terms in terms of n? Do some algebra to combine them.
     
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