A and B are playing a dice game with one dice. A starts the game first. 6 will win. What is

the probability that A will win the game?

I found the answer by the help of 1/1-n,using series and limit. The answer is 6/11. But there is another solution and I can't understand the logic of it.The solution is as follows:

A starts first.The probability that A will win is "x".

The probability that B will win is 5

-----.x

6

x + (5/6)x= 1 x=6/11

There is also another solution:

x= (1/6)(1) + (5/6)(5/6)u

x[1 - 25/36] = 1/6

x(11/36) = 1/6

x = 6/11