Given

$x_k=\frac{L_k}{\sqrt[\phantom{2}]{L_k\sqrt[\phantom{2}]{L_k\sqrt[\phantom{2}]{L_k+8{}^3}}}}$

where

$L_k=1+\frac{1}{1+\frac{1}{k}},k=1,2,$dots,$50.$

Use GNU Octave to compute

$S=x*L={\displaystyle \underset{k=1}{\overset{50}{}}}{x}_k{L}_k.$