Why do this problem ?

The problem gives a neat application involving the manipulation of surds where surds occur in the denominator of a fraction.

It makes a good rounding-off to the section of work on surds which includes rationalisation of denominators.

Possible approach

This is a short problem that can be used as a lesson starter to a lesson on surds or on summing series.

Key question

Can you simplify the fractions with the surds in the denominators?