Question

If `{(n-1)!+n!}/((n+1)!) =1/6`, find `n`?

Answer 1

`n=6`

Explanation:

`{(n-1)!+n!}/((n+1)!) =1/6`

`hArr{(n-1)!+n(n-1)!}/(n(n+1)xx(n-1)!) =1/6`

or `((n-1)!(1+n))/((n-1)!(n^2+n)) =1/6`

or `(1+n)/(n^2+n)=1/6`

or `n^2+n=6+6n`

or `n^2-5n-6=0`

i.e. `(n-6)(n+1)=0`

i.e. `n=6` or `-1`

But as `(-1)!` is not defined `n=6`