2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122397We discuss the summation of certain series defined by counting blocks of digits in the $B$-ary expansion of an integer. For example, if $s_2(n)$ denotes the sum of the base-2 digits of $n$, we show that $\sum_{n \geq 1} s_2(n)/(2n(2n+1)) = (γ+ \log \frac{4}π)/2$. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.12 pages, Introduction expanded, references added, accepted by J. Number TheoryNumber Theory11A63, 11Y60text