id: 06494821
dt: j
an: 2015f.00808
au: Ramsay, Ian
ti: Finding formulae for summing the general power series of positive integers.
so: Math. Teach. (Derby) 238, 17-21 (2014).
py: 2014
pu: Association of Teachers of Mathematics (ATM), Derby
la: EN
cc: I30
ut: power series of natural numbers; integers; sum; manipulation of
expressions; polynomials; equations; simultaneous equations;
coefficients; powers; leap-frog pattern-recognition method; Fermatâ€™s
last theorem
ci:
li:
ab: 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.
rv: