Recursion

Recursion is a method of problem solving in which you break apart a problem into less complex instances of itself in an attempt to find solution. This will hopefully break down into a simple base case which once solved can solved a more complex iteration of the problem, eventually leading up to the solution of the original problem.

In my experiences, recursion has been more like... trying to break down a problem into a simpler form and ending up confused for a few hours. Lately this has become easier as struggling with it during the assignment forced me to think about it in different ways, leading me to a way of breaking down the original problem that seems to work better for me. Instead of thinking of a slightly simpler instance of it, I try and imagine what steps are involved and how they link together.

As for the power of recursion, it does indeed simplify problems once you obtain a recursive formula or algorithm as it automates the process of solving the problem and you can simply extend the formula for specific cases.