How do I show that
$ \frac{1}{1}-\frac{1}{4}+\frac{1}{7}-\frac{1}{10}+\ldots= \frac{1}{3} \left( {\frac{\pi}{\sqrt{3}}+ \log 2} \right)?$
This problem belongs to Riemann Theory of Definite Integral, and not to any series summation. I recommend an answer which is to the topic i.e., Riemann Theory of D.I..
Thanks!