The Delian League was formed so that the Greek city-states fight together against the Persians.
Step-by-step explanation:
The Delian League was formed by the suggestion of Athens. The purpose of Athens was to fight the Persians even after the war officially ended. The Greek city-states accepted the proposal of Athens and they created the Delian League.
Athens though, despite being the one that initiated the formation, was actually the one that caused the crumbling of the Delian League. The reason was that Athens started to use the funds of the Delian League for its own purposes, so once the other city-states found out about this they got into conflict with Athens. Things escalated when Sparta got involved, with a war between Sparta and Athens emerging, known as the Peloponnesian War, which put an end to the Delian League.