Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / 19 / c / i

There is an indexing defect in the original PDF: the term at $n=1$ is undefined because $\ln 1=0$. Thus the series as literally indexed is not defined. The natural finite-index repair is to start at $n=2$, and that repaired series still diverges.

Indeed, for $n\ge 2$ the terms are positive andThey eventually increase at a geometric rate and do not tend to zero. Since the terms of a convergent series tend to zero, no choice of a finite replacement for the missing first term could make the tail converge.