I was recently introduced to Finite Calculus through Graham and Knuth. I stumbled upon this sum earlier today in a problem posted in this site, although I cannot link to it right now because I'm on the mobile app. I just wanted to know if it is possible to analyze it through calculus
The sum is $$ \sum_0^M \frac {(n^2)_x}{(n)^{x+1}} dx$$
Where I use $(n)_x$ for the falling factorial power and $(n)^x$ for the rising factorial
I know this is way out of my league (because I just started reading on the subject), I just want to know if it's possible to find a solution
Thanks in advance!