Finding the remainder of $N= 10^{10}+10^{100}+10^{1000}+\cdots+10^{10000000}$ divided by $7$ $$N= 10^{10}+10^{100}+10^{1000}+\cdots+10^{10000000}$$. What is the remainder when N is divided by 7?
$$N=(10^{10}+10^{100}+10^{1000}+\cdots+10^{10000000})/7$$
$$Rem[3^{10}+3^{100}+\cdots+3^{10000000}]/7$$
Now I did not understand it from the next step
Now in the next step it has been given
$Rem[3\cdot 3^9+3\cdot3^{99}+\cdots+3\cdot3^{9999999}]/7$
$Rem[\underbrace{(-3)+(-3)+\cdots(-3)}_{7~\text{times}}]/7$

3^9 is a multiple of 3^3 which can be written as 27 and what is 27=28-1 now if you divide 27 by 7 what is the remainder?. It is -1 so now you multiply it with 3 in every step 
so= $-3 (7times )/7$
