Knuth's series is given by
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
(OEIS A096616), where 
is the Riemann zeta
function (Knuth 2000; Borwein et al. 2004, pp. 15-17).
Knuth's Series
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References
Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 16 and 221, 2007.Borwein, J.; Bailey, D.; and Girgensohn, R. "Knuth's Series Problem." §1.5 in Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, pp. 15-17, 2004.Knuth, D. E. "Problem 10832." Amer. Math. Monthly 107, 863, 2000.Sloane, N. J. A. Sequence A096616 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Knuth's SeriesCite this as:
Weisstein, Eric W. "Knuth's Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KnuthsSeries.html