In this sentence, is this
疲れて explaining the reason? Why was he not able to study? Why can't we use
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You could use ので or から, you just don't have to as it can be implied. Compare «I was tired yesterday and I couldn't study» vs «Because I was tired yesterday I couldn't study». Your example is essentially the former.
The いて is the te-form of いる which marks the verb as progressive or ongoing.
疲れる — To be tired
疲れている — Is tired
疲れていて — te-form of being tired