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(Solved): 1. Prove that the sum of any 2 consecutive triangular numbers is a square number. (Note: a direct c ...
1. Prove that the sum of any 2 consecutive triangular numbers is a square number. (Note: a direct calculation may work better than induction here. A picture proof is also possible) 2. Prove the identity ?i=1n?Fi2?=Fn?Fn+1?, where Fn? indicates the nth Fibonacci number.