On Sunday, February 10, 2013 8:35:32 PM UTC-8, vv wrote: > I'd be grateful if someone can throw light on whether or not the > > following series is uniformly convergent for x not equal to zero: > > > > \sum_{n=1}^infty exp(-ixn)/n

It might help to look at the Taylor series with remainder formula for -log(1-y) and let y = exp(-ix)