No matter how much I try I cannot understand the intuition behind this formula. I do not understand why there is a $1$ to begin with, and I do not understand why you multiply all probabilities by $u$ from that state to the absorbing state.
With my logic I think it is about the expected number of steps until reaching the absorbing state. So, If $u$ is the expected number of steps from state $j$ to the absorbing state, how does this give you the expected time from that state to the absorbing state? Please someone give me intuitive reasoning and an example.
Talking about this formula: