OFFSET
1,1
COMMENTS
This sequence provides insight into the manner of convergence of sum{(h^2)/2^h, h = 1..k} to 6.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Let s(n) = 6 - sum{(h^2)/2^h, h = 1..n}. Approximations follow:
n ... s(n) ........ 1/3^n
1 ... 5.50000 ... 0.333333
2 ... 4.50000 ... 0.111111
3 ... 3.37500 ... 0.037037
4 ... 2.37500 ... 0.012345
5 ... 1.59375 ... 0.004115
6 ... 1.03125 ... 0.001371
7 ... 0.64843 ... 0.000457
8 ... 0.39843 ... 0.000152
9 ... 0.24023 ... 0.000050
10 .. 0.14257 ... 0.000018
11 .. 0.08349 ... 0.000006
a(2) = 11 because s(11) < 1/9 < s(10).
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 10 2014
STATUS
approved