Terry had to be dumber in the beginning to make Bruce relevant. In later episodes Terry trained in martial arts with one of Bruce's teachers, and if you'll remember the JL wanted Batman on their team because of his outsider looking in approach. Later on in Epilogue they wanted him for his detective skills. 

In the comics... in Batman Beyond 2.0 that was still mostly based on the cartoon and the comic series spun out of it... Terry was in college and relying on Bruce a lot less. He was also a more integral part of the JL in JL Beyond 2.0. 

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