I'm looking at a Project Euler problem, where a harmonic series is modified such that it excludes terms where a digit appears three times consecutively in the denominator. So this series would exclude 1/111, 1/222, 1/1000, 1/1112, 1/2221, etc.
It turns out that this series is convergent, albeit very, very slowly. If I need to calculate the sum of this series up to 10 decimal places of accuracy, is there a way of doing this without brute force?
Thank you.