Maths Help !?

1+1/2+1/4+1/8+....is
1+1/2+(1/2)^2+(1/2)^3+.... is a geometric series with first term a =1 and common ratio r=1/2
The sum is a/(1-r)
= 1 /(1-1/2) = 1/(1/2) = 2

-2G (2) = -4G

Don't worry it's pretty easy.
In the second last step, they took -2G common outside. So you will be left with whatever is in the brackets. If you open the bracket, you'll go back to the third last step. So basically they just simplified it.
Now whatever is left in the bracket forms an infinite GP (geometric progression). And the sum of infinite GP can be given as Sum=a/(1-r)
[where a=first term, r=common ratio]. So they applied this formula in the last step.
Hope i helped :)

First circled step: collecting terms and factoring out -2G.
Second circled step: the infinite sum of a*r^(n-1) = a/(1-r) where |r|<1. Here a=1 and r = 1/2.