Accelerating the convergence of an infinite series
John Klippert · International Journal of Mathematical Education in Science and Technology · 1984
is a power series with positive radius of convergence, we find that where xeD, the domain of convergence (x ? 1), and ? an = an+1— an. This identity leads to a transform which can accelerate the convergence of the series or, in the case that an = P(n), a polynomial sequence, give us a closed form for the series.