Considering the number $\frac{3}{7}$ written under the form $\frac{3}{7} = 0,a_1a_2a_3\dots$ compute $a_1+a_2+a_3+\dots+a_{2013}$

Question

I have a problem that I don't know how to solve: Considering the number $\frac{3}{7}$ written under the form $\frac{3}{7} = 0,a_1a_2a_3\dots$ compute $a_1+a_2+a_3+\dots+a_{2013}$.

I've only computed the number $\frac{3}{7}$...$\frac{3}{7}=(428571)$ but from here I don't know what to do anymore.

Answer 1

Since we have $$2013 = 335\cdot 6+3$$

the sum is $$335\cdot (4+2+8+5+7+1)+4+2+8=9059$$

Answer 2

$$a_1+a_2+...+a_{2013}\\=a_1+a_2+...+a_{2010}+a_{2011}+a_{2012}+a_{2013}\\=335\times (4+2+8+5+7+1)+4+2+8\\=9045+4+2+8=9059$$