Sum

This sum if really a combination of 2 geometric series.

First geometric series: $1\over{5}$,$2\over{25}$,$4\over{125}$, and so on

Second geometric series: $2\over{5}$, $4\over{25}$, $8\over{125}$, and so on

use: $a_1\over1-r$ formula: The sum of the first geometric series would be: $1\over{5}$$\div$$3\over5$=1/3

2nd would be: 2/5 $\div$ 3/5 = 2/3

1/3+2/3 = 1

We still didn't add the first term: 1

So 1+1 = 2

Nice, AD  !!!!