0
$\begingroup$

Do a convergence tests for the following series.

$$\sum_{n=1}^{\infty} \frac{\log^{100}n}{n}\sin\frac{(2n+1)\pi}{2}$$

I have one more question how can i show convergence with alternating series test (Leibniz's test)?

  • 1
    You can simplify the $\sin$: a known convergence test will appear.2012-05-30
  • 1
    It is usually recommended that you give your thoughts on the matter, so that your fellow users might be directed properly when answering your inquiry. It is also considered ungentle to use the imperative.2012-05-30
  • 3
    While Dirichlet's test is dandy, a beginning Calculus student might notice the $\sin$ terms give alternating signs, and then go on to use the Alternating Series Test, as hinted by Davide and Marvis.2012-05-30
  • 0
    Peter - you've right. I'm sorry but i'm not fluent in english especially math equation and i can't share my ideas how i can do this task. Thanks for answears, now i start analyze this and i hope so i understand this;)2012-05-30

2 Answers 2