On the continued fraction $\frac{1 |}{| z } +\frac{1 |}{| 1 } + \frac{2 |}{| z } +\frac{3 |}{| 1 } + \frac{4 |}{| z} + \cdots$

Abstract

The article on hand deals with the continued fraction

$$\frac{1 |}{| z } +\frac{1 |}{| 1 } + \frac{2 |}{| z } +\frac{3 |}{| 1 } + \frac{4 |}{| z} + \cdots.$$

The famous Indian mathematician Srinivasa Ramanujan has given a pre-presentation by a power series, but he however concealed a proof. Subsequently a proof has been established, but a direct verification is intricate. Here we give a quick and direct approach with comparitively little effort.