Answer
$S_6=39060$
Work Step by Step
We need to find:
$\sum_{k=1}^{6}10*5^{k-1}$
We see that this is a geometric sequence with $a=10$ and $r=5$.
We know the partial sum of a geometric sequence is:
$S_n=a_1\frac{1-r^n}{1-r}$
$S_6=10\frac{1-5^{6}}{1-5}=39060$