I need some help.

I have a statistic question about Markov chain:

Consider the continuous time Markov chain on teh nonnegative intergers
which moves from state n to state n+1  at rate rn, suppose it starts
in state 0.  What is the characteristic function of the time, Tn that
the chain first reaches state n? Invert the characteristics function
to find the distribution of the arrival time for n=3. Assume r(j)
distinct.

Thank you very much
Cyn

Continuous time markov chains can be tricky; this seems like it is
closer to a $15.00 question actually.