Testing convergence of sequence

[jlu]

how can i can the convergence of sum[sin (0.4)n / n pi]2 and that sum[sin (0.4)n / n pi] diverges, n is between -infinity and + infinity

 

[mathman]

how can i can the convergence of sum[sin (0.4)n / n pi]2 and that sum[sin (0.4)n / n pi] diverges, n is between -infinity and + infinity

The first series converges because it is dominated by 1/n^2 series, which is convergent. The second is harder - the 1/|n| series diverges, but this is only a clue.

 

[jlu]

i used p-series test for the first one and root test for the second one. i stand to be corrected if i used the wrong rules