A337911 Decimal expansion of probability that the random harmonic series converges to 0.

2, 4, 9, 9, 1, 5, 0, 3, 9

Offset

0,1

Comments

Define g(0, x) = 1/4 if -2 <= x <= 2, otherwise g(0, x) = 0; g(n, x) = Integral_{y=x - 2/(2*n+1)..x + 2/(2*n+1)} g(n - 1, y)*(2*n+1)/4 dy for n > 0. With t_i being independent random variables with common distribution P(t_i = 1) = P(t_i = -1) = 1/2, the probability of random harmonic series Sum_{i>=1} (t_i)/i converging to x is lim_{n->infinity} g(n, x).

Links

Table of n, a(n) for n=0..8.

Byron Schmuland, Random Harmonic Series, The American Mathematical Monthly, Vol. 110, No. 5 (May, 2003), pp. 407-416.

Example

0.249915039...

Crossrefs

Sequence in context: A340169 A079781 A163299 * A198679 A244285 A111422

Adjacent sequences: A337908 A337909 A337910 * A337912 A337913 A337914

Keyword

nonn,cons,more

Author

Jinyuan Wang, Oct 02 2020

Status

approved