The discussion focuses on identifying geometric progressions starting from one that sum to a perfect square. A specific example provided is the series 1 + 3 + 9 + 27 + 81, which equals 121, a perfect square (11^2). Participants suggest using spreadsheets for experimentation and reference the Wikipedia page on geometric progressions for formulas. Additionally, considering the differences between subsequent squares is recommended as a method to find valid sequences.
PREREQUISITESMathematicians, educators, students studying sequences, and anyone interested in the properties of geometric progressions and perfect squares.
Try considering the sequence of squares, 0, 1, 4, 9, ..., and take the difference between subsequent squares. That will help you find the answer.Medtner said:"Write out a series of three or more different whole numbers in geometric progression, starting from one, so that the numbers should add up to a square. So like, 1 + 2 + 4 + 8 + 16 + 32 = 63 (one short of a square)"(can't find an actual real life example)
I can't seem to find an answer for this?