(34C) (11C) Summation of Infinite Alternating Series

[Albert Chan]

Hi, robve

Let the last 3 cumulative sum of s2 be a, b, c

a + t[d] = b
b + t[d+1] = c = s2

Aitken(a,b,c) = c - (c-b)^2/((c-b)-(b-a)) = s2 - t[d+1]^2 / (t[d+1] - t[d])

Or, Secant's method, from 2 points: (x1, y1) = (b, t[d]), (x2, y2) = (c, t[d+1])
Extrapolate for (x, t[∞] = 0). Both methods are equivalent.

x = x2 - y2 * (x2-x1)/(y2-y1) = s2 - t[d+1]^2 / (t[d+1] - t[d])