Discussion: This student has done an excellent job investigating this expressions by working out the sum for ten cases. It is noticed that the numbers that arise are identical with the Fibonacci sequence and it is conjectured that this pattern persists. The student attempts to prove this by mathematical induction but it is not quite formulated correctly.

Written response: Good investigation and pattern recognition. I don't follow the rest of it. Try going back to the binomial recursion and make use of this to formulate and prove your induction.

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