- #1

freshman2013

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## Homework Statement

Here are some series I'm completely stuck on.

1.sqrt(n)*(1-cos(1/n))

2. a series in which if n is odd, then a

_{n}is 1/(n+[itex]\sqrt[]{n}[/itex]) while if n is even, then a

_{n}is -1/n

## Homework Equations

## The Attempt at a Solution

For 1., I tried integral test which seemed impossible to integrate, and then I tried comparison test but i can't find anything to compare to

For 2. I thought that as n approaches infinity for 1/(n+[itex]\sqrt[]{n}[/itex]), which equals (1/[itex]\sqrt{n}[/itex])/([itex]\sqrt{n}[/itex]+1), then that expression pretty much looks like 1/n and thus the series is approx (-1)^n/n and is thus conditionally convergent like (-1)^n/n. But I then realized perhaps you can't apply the alternating series test since in the original series, the abs value of it is not decreasing for every term.E.g.1/(100+root(100))=1/110 < 1/101 Anyone have any idea on how to tackle this, or am I right from my original attempt?

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