Hee, I got a really simple recurrence relation:

$\displaystyle \lambda_n=2-\frac{1}{\lambda_{n-1}}$ with $\displaystyle \lambda_1=2$.

Calculating a few values we easily notice $\displaystyle \lambda_n = \frac{n+1}{n}$,

but how is this formally derived?

Can someone offer a quick insight?