unfair die no of trials sum

Hey all,

i am trying to solve a problem but somehow either my brain is dead right now or the problem is hard. The actual problem is something related to communication networks but it can be modeled for this purpose by a repeated die throw. So the problem is as follows

I have a discrete random variable X with some pmf . Now we perform repeated trials and define a Random variable as the sum of all the outcomes . now i want to find the probability that i will exceed some specified value N at kth trial...for different values of k ...i.e k is a randomo variable whose distribution is required to be calculated...

if its the other way round i.e k is fixed and we need to find the distribution of N then by applying central limit theorem i can do that (assuming K large enough ) but here i am kind of stuck.....Thanks for your help in advance