Measure Theory-Lebesguq Measure

WannaBe22

1. The problem statement, all variables and given/known data
Prove the set [tex] A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} ) [/tex] is Lebesgue measurable and calculate its measure.


2. Relevant equations
3. 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
[tex]A= (\frac{1}{5}, \infty)[/tex]