Question

Find x in each of the following:
(iii) $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$

Answer 1

Given: $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$
$\Rightarrow \frac{1}{6!}+\frac{1}{7\times 6!}=\frac{x}{8!}$
Taking L.C.M
$\Rightarrow \frac{1+7}{7\times 6!}=\frac{x}{8!}$
$\Rightarrow \frac{8}{7!}=\frac{x}{8!}$
$\Rightarrow \frac{8}{7!}=\frac{x}{8\times 7!}[\because n!=n(n-1)!]$
$\Rightarrow x=\frac{8\times 8\times 7!}{7!}$
$\Rightarrow x=64$