Closed form for finite summation of sequence $\sum^n_{i=1}{e^i/i}$ Does there exist a closed form for finite summation of the sequence  $\sum^n_{i=1}{e^i/i}$ ?
Take the derivative of the function $f(x) = \sum_{i = 1}^n \frac{x^i}{i}$ which is easier to compute.
Maple writes it as $$\sum_{i=1}^n \frac{{\rm e}^i}{i} = -\Phi \left( {{\rm e}},1,n \right)\; {{\rm e}^{n}}-\ln 
 \left( -{{\rm e}}+1 \right) +{\frac {{{\rm e}^{n}}}{n}}$$

where $\Phi$ is the Lerch Phi function.