As a follow up of my previous question here is an improved version of the series:
$\sum_{i=1}^{2NR}{i\cdot \left( \dfrac{1}{1-p} \right)^i}\, \left(1-\dfrac{2R-(2NR-i)\Delta}{2R} \right) $
where:
- $p\in [0,1]$
- $R\in [0,1]$
- $N$ positive integer
- $\Delta$ infinitesimal
Notice that for $i=2NR$ the last term of the series, that is actually a probability, is 0 and it is correct.
My question is: it is possible to get a closed form expression?