There is something i do not quite understand when it comes to learning math. There are problems were you just have to find connections and i can't understand how to do all of those connections. For example look at this question: http://math.stackexchange.com/questions/294213/prove-that-13-23-n3-1-2-n2
You can use the $(a+b^2)$ relation or the mean value of the first and last item in the sum.