hello everybody, about that formula for 1/pi, it is nice , the coefficient a(k) is a binomial term The sequence a(k) is : 1, 1, 33, 97, 1729, 8001, 105441, 627873, 6989697, 48363649, 488206753, 3701949153, 35289342529, 283146701761, 2610495177057, 21695983405857, 196218339243777, 1667338615773441, 14917038493453089, 128562758660255073, 1143482133220664769, 9946278255903268929, 88205310329762729697, 771946983805271894433, 6837125121111415598721,... Which has this g.f. 1 -------------------- = 2 1/2 (1 - 2 x - 63 x ) Now, this has a closed binomial expression, of course anyhow, this series : can be programmed into : proc(k) local x; (x^2 + x + 16)^k; expand(%); coeff(%, x, k) end; and proc(k) (30*k + 7)*binomial(2*k, k)^2/(-256)^k;%*f(k); end; which gives a sequence : which converges to 24/Pi at a rate of approx. .25 digits per term. or in other words, 1000 terms = 250 digits of precision. best regards, Simon Plouffe