Measure Theory-Lebesguq Measure

[WannaBe22]

Homework Statement

Prove the set $$A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} )$$ is Lebesgue measurable and calculate its measure.

Homework Equations

The Attempt at a Solution

I've proved the set is measurable...But how can I calculate its measure?


I will be delighted to get some guidance

Thanks in advance !

 

[HallsofIvy]

It looks to me like
$$A= (\frac{1}{5}, \infty)$$