Consider the series . Let $\displaystyle s_n$ be the n-th partial sum; that is,
s4=
s8=
can someone help me with this one
you could use brute force to attack the problem...
$\displaystyle s_{1}=10(\frac{1}{8})$
$\displaystyle s_{2}=10(\frac{1}{9}+\frac{1}{8})$
...
$\displaystyle s_{4}=10(\frac{1}{11}+\frac{1}{10}+\frac{1}{9}+\fr ac{1}{8})$
there could be a simpler way, the only thing bothering me is that
$\displaystyle \sum^{\infty}_{n=1}\frac{10}{n+7}$
should diverge since
$\displaystyle \sum^{\infty}_{n=1}\frac{1}{n}$ diverges