Sharedgeom_series.sagewsOpen in CoCalc
Author: Matt Thomas
a(n) = 1/(n^2+3*n+2) [a(n) for n in [1..10]]
[1/6, 1/12, 1/20, 1/30, 1/42, 1/56, 1/72, 1/90, 1/110, 1/132]
sum([a(n) for n in [1..10]])
5/12
(5-(5*3^(10)))/-2
147620
def s(k): return sum([a(i) for i in [1..k]])
[s(k) for k in [1..10]]
[1/6, 1/4, 3/10, 1/3, 5/14, 3/8, 7/18, 2/5, 9/22, 5/12]
list_plot([s(k) for k in [1..100]], pointsize=50)
L = [s(i) for i in [1..25]] L
[15, 60, 195, 600, 1815, 5460, 16395, 49200, 147615, 442860, 1328595, 3985800, 11957415, 35872260, 107616795, 322850400, 968551215, 2905653660, 8716960995, 26150883000, 78452649015, 235357947060, 706073841195, 2118221523600, 6354664570815]
list_plot(L, pointsize=50, color="green")