Some Formulae of S. Ramanujan IV

Abstract

In 1917, S. Ramanujan [6] submitted, as a problem to this journal, the following result:
Log 2∑(-1)^k/k Log K+Log²2∑1/k log K log (2k)=1. (1.1)
This also appears in chapter 13 of his Second Note book and, for a solution, we refer to [6] (unavailable to the author) and B.C. Berndt (cf. [1], p. 217). Here we present another solution based on the following Lemma.