On a Series of Goldbach and Euler.

The article focuses on the a theorem about an infinite series which was communicated by Christian Goldbach to Leonhard Euler and is one of the theorems mentioned in Euler's paper "Variae observationes circa series infinitas." Goldbach and Euler's proof is a common example of what some historians consider a misuse of divergent series because it begins by assigning a value to the harmonic series Σ1/n and is then manipulated by subtractions and replacement of other series until the desired result is attained. The proof of the theorem is hereby reviewed in order to vindicate Goldbach and Euler's work. It is shown how the deficiency in the proof can be amended. However, other results obtained in said Euler's paper are not as easily amended.