$\displaystyle \sum_{i=1}^n \frac{x^i}{i} $

how to change this summation into a definite integral ???

$\displaystyle \sum_{i=1}^n x^{i-1} = \frac{1}{1-x} $

integrate both sides, LHS will have $\displaystyle \sum_{i=1}^n \frac{x^i}{i} $

but what is the definite limit to take???

thanks