Question: Integration for finding k-th probability

Hello Maple experts,

 I want to find out k-th probability (denoted by c(k)) which is expressed as an integration of summation for values ranging from j=0 to k. The function is very complicated , I have attached the PDF for expressing the mathematical term properly.

I am able to find out the c(k) for a given value of k, if k is specified in the beginning of the maple program. But I am unable to make it generic form of k.

I have also attached the Maple code. I have searched a lot in this website before posting. Please help me.

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