Prove the following equality of sets

Hi,I'm a bit struggling with this question from my Analysis practice.

Can anyone please help me with it?

Here is the question:

Prove the following equality of sets:

(Large Union)for n=0 to infinite = (0,1/(n+1)]=(0,1]

Some people suggested that when try to prove two sets equal to each other, try to prove first one include in the second one,and second one include in the first one.So I tried,and I can prove (0,1/(n+1)] is in (0,1], but I cannot prove the other way around.