Discussion: A complete solution is given to this problem. First, the student does a comprehensive investigation and through very detailed pattern analysis conjectures a formula. A recursion formula is developed and then, induction is used, and executed correctly, to demonstrate the truth of the conjecture.

Written response: Very nice treatment. All the elements of a good solution are here. You investigated the problem and got a summation formula and applied it to some small values of n. Then you saw a closed formula arising. Nice job of finding a recursion and then using it to prove your formula by induction.

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