1: Isn't exactly infinite series if there are just 2 panes.
If you let the intensity of incident light be 400
1/4th is transmitted from pane 1, or intensity of transmitted is 100
This 100 intensity light is now the incident on second pane.
Again 1/4 th is transmitted so the final intensity is 100/4 =25
in general it's going to be (x/4)^n where x is intensity of initial ray and n is the number of panes.
2: You are walking at a speed of 1m/s and the rope is supposedly lengthening by 1000m/s
so say you are able to cross it after 't' seconds.
that would be possible if
(t)*(1 m/s) = 1000+[(1000m/s)*(t)] (since initial length of ope is 1000m and it is lengthening by 1000m/s)
which fives a t<0, which is not possible.
Hence you can not cross it even if you were God.