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## Homework Statement

Not really sure where tou go with this one.

## Homework Equations

If the nth partial sum of a partial series is given by,

Sn= [tex]\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}[/tex] = [tex]\sum_{k=1}^{n}[/tex][tex]\frac{1}{n+k}[/tex]

a) write the associated series

b) test for convergence

c) if possible, determine its limit

## The Attempt at a Solution

Here is what I have come up with:

[tex]s_1[/tex]=1/2

[tex]s_2[/tex]=1/2+1/3+1/4

[tex]s_3[/tex]=1/2+1/3+1/4+1/5+1/6

[tex]a_n = \left\{ \begin{array}{c} \frac{1}{2} \text{ for }n=1 \\ \frac{1}{2n-1}+\frac{1}{2n} \text{ for }n\geq 2 \end{array} \right.

[/tex]

I don't know what to do next. What do I do with the 1/2?

I am pretty sure I can handle b and c, I just need help with a.

Thanks in advance!