Question

Let X1, X2, ... be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to be the smallest k such that X1 + X2 + ... + Xx exceeds cn = 5 + 12/n, namely, Nn = min{k >1: X1 + X2 +...+Xk > cn} Does the limit lim P (NK>n) 100 exist? If yes, enter its numerical value. If not, enter -999.