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anonymous
 5 years ago
Does the series converge or diverge?
Sum (n*cos(1/n))/(sqrt(n^51)), n>1 to infinity.
anonymous
 5 years ago
Does the series converge or diverge? Sum (n*cos(1/n))/(sqrt(n^51)), n>1 to infinity.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first note that cos(1/n) is always between 1 and 1. then we see that our bn = (n*1)/(n^(5/2)) which is always going to be bigger then the original series. bn then simplifies down to 1/(n^(3/2)), which is a p series where 3/2 is bigger then 1 and therefore convergent thus by basic comparison test the original series converges
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