Finding formulae for summing the general power series of positive integers. (English)

Math. Teach. (Derby) 238, 17-21 (2014).

Summary: The author proposes a conjecture. Specific formulae for summing power series up to the 25th power are derived using pattern recognition. Equations allowing the sum to be calculated for the general even power and then easily for the general odd power are also derived. The solution depends on distinguishing between sets of well-behaved and badly-behaved functions. Taming the badly behaved functions is the key. A conjecture akin to Fermatâ€™s.