# Math Help - partial sums of series

1. ## partial sums of series

Consider the series . Let $s_n$ be the n-th partial sum; that is,

s4=
s8=

can someone help me with this one

2. This is just plug and chug. You got to do for yourself.
$S_4 = \frac{{10}}
{8} + \frac{{10}}
{9} + \frac{{10}}
{{10}} + \frac{{10}}
{{11}} = ?
$

3. you could use brute force to attack the problem...
$s_{1}=10(\frac{1}{8})$
$s_{2}=10(\frac{1}{9}+\frac{1}{8})$
...
$s_{4}=10(\frac{1}{11}+\frac{1}{10}+\frac{1}{9}+\fr ac{1}{8})$

there could be a simpler way, the only thing bothering me is that
$\sum^{\infty}_{n=1}\frac{10}{n+7}$
should diverge since
$\sum^{\infty}_{n=1}\frac{1}{n}$ diverges