Originally Posted by

**Anemori** i hope this is the right place:

Find the sum of:

$\displaystyle \sum_{n=1} ^{10} {3*(\frac{1}{4})^n}$

$\displaystyle =1-(\frac{1}{4})^{10}) = 1 $

but there is an additional problem:

Find the error between $\displaystyle S_{10}$ and $\displaystyle s_\infty$. Use the formula for $\displaystyle S_n $ and $\displaystyle s_\infty$ of convergement geometric series , find a general formula that gives the error between $\displaystyle S_n $ and $\displaystyle s_\infty$. Use the new formula to explain why, for the series in #7, the error between $\displaystyle S_n $ and $\displaystyle s_\infty$ is always equal to $\displaystyle r^n$.

I don't understand the problem. please help me out! thanks!