I'm an economics student stuck on this dynamic optimization problem, where the second part of the problem includes "mathematical induction". I think I have understood the notion of it (the two cases that I need to test), but I have no idea how to apply it here. Anyways, any help/pointers are very welcome!
The problem: https://studentweb2.hhs.se/courseWeb.../PS6(2012).pdf
I think I have found the correct general function (see the attached PDF), but the induction part is beyond me!