2. A TV station is going to broadcast a 30-episode TV series. If it is required that the number of episodes aired each day must be different, what is the maximum number of days the TV series can be broadcast?

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2.【Solution】If it is broadcast for more than 8 days, then since the number of episodes broadcast each day is different, there must be at least $1+2+3+4+5+6+7+8=36$ episodes,

so a 30-episode series cannot be broadcast for more than 8 days as required. On the other hand, $1+2+3+4+5+6+9=30$

so it can be broadcast for a maximum of 7 days, with the number of episodes broadcast each day being $1,2,3,4,5,6,9$.