x + $\frac{1}{2}$ + $\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{47}{42}$
x + ($\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + $\frac{1}{5.6}$) = $\frac{47}{42}$
x + (1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ +...+ $\frac{1}{5}$ - $\frac{1}{6}$) = $\frac{47}{42}$
x + ( 1 - $\frac{1}{6}$) = $\frac{47}{42}$
x + $\frac{5}{6}$ = $\frac{47}{42}$
x = $\frac{47}{42}$ - $\frac{5}{6}$
x = $\frac{2}{7}$
