I have the series: $$\sum_{i=1}^{i=10^N} \log_5 i$$ I'm trying to figure out how to get the closed-form solution to this problem. I entered it into WolframAlpha and got that it equals: $ (\log(\mathrm{Pochhammer}(1, 10^N)))/(\log(5))$
I have a few things I'm not understanding about this problem,
- What procedure do you use to find a closed-form solution here?
- What does this solution even mean? (I've never seen this pochhammer symbol)
- If possible, could someone tell me if there's any general method for solving these types of problems? I have a lot of them and have been messing around with some algebra, but don't really even understand how to start them. It seems like I'm just having to google until I find some identity that looks similar enough in form. This is for a programming course, but I have no background in algorithms so I'm struggling a bit.