Given n ∈ N s.t. 2n+1 is a perfect square. Prove n+1 is the sum of two consecutive perfect squares.

Intriguing proof from Loren C. Larson's book "Problem-Solving through Problems". Interview conducted by math educator/enthusiast, Deanna Haunsperger, yields thought provoking insight regarding mankind's obsession with mathematics. Go Knights!! Visual proof of Sum = n/(n+1)/2 triangular numbers with cannonballs! collaboration with Stephen F. Kennedy