What are some strategies for trying to determine the general formula for a summation?
For example, let's say I'm trying to determine the general formula for
I was not sure how to approach this question, so I plugged and tested several values of $n$ in order to determine a pattern, and determined that:
However, I feel that there are probably more efficient and reliable ways to solve these types of questions other than inserting values and finding patterns. If anyone has any guidance, it would be greatly appreciated!