$\sum_{k=2} \frac{1}{(k-1)^2} + k^{-2} * \log{k}$
Also you did not provide enough information for us to help you fully. The above is the summation of series terms $a_n$ as $k\to\infty$, If you want to find the sum of this series you must determine if the series converges, else wise it diverges and your limit is not finite so will not have a sum for the series as it goes to infinity