Question

The remainder when 1010 + 10100 + 101000 + ... + 1010000000000 is divided by 7 is

Answer 1

Answer:

Step-by-step explanation:

Easiest method to solve this question :

Here it is-

10^10+10^100+10^1000+.……+10^10000000000 / 7

We can write this as-

(7+3)^10+(7+3)^100+(7+3)^1000+……….+(7+3)^10000000000 / 7

Now, (7+3)^10 /7 = 3^10 /7 = 4

(7+3)^100 /7 = 3^100 /7 = 4

(7+3)^1000 /7 = 3^1000 /7 = 4