OFFSET
1,2
COMMENTS
Adding the series -1+sqrt(2)-3^(1/3)+4^(1/4)..., according to this sequence, 10 billion terms must be added to arrive at 11 accurate digits of the MRB constant.
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 450. ISBN 0521818052.
LINKS
Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, Convergence Acceleration of Alternating Series, Experimental Mathematics, 9:1 (2000).
Eric Weisstein's World of Mathematics, MRB Constant.
Wikipedia, Mathematical constant
EXAMPLE
For n=1, a(n)=1 because after 10^1 partial sums of -1+sqrt(2)-3^(1/3)+4^(1/4)... you get one accurate digit of the MRB constant.
For n=2, a(n)=2 because after 10^2 partial sums you get two accurate digits and so on.
MATHEMATICA
m = NSum[(-1)^n*(n^(1/n) - 1), {n, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> 1000]; Table[-Floor[Log[10, Abs[m - NSum[(-1)^n*(n^(1/n) - 1), {n, 10^a}, Method ->"AlternatingSigns", WorkingPrecision -> 1000]]]], {a, 1, 50}]
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Marvin Ray Burns, May 25 2009
EXTENSIONS
Corrections from Marvin Ray Burns, Jun 05 2009
Link to Wikipedia replaced by up-to-date version; keyword:less added R. J. Mathar, Aug 04 2010
Corrections by Marvin Ray Burns, Aug 21 2010, Jul 15 2012
STATUS
approved