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 A205326 Decimal expansion of the sum of [0;n,n,n,...]^2 for n=1..infinity. 1
 9, 1, 5, 5, 8, 7, 9, 1, 9, 9, 0, 1, 8, 1, 9, 7, 2, 5, 1, 9, 9, 8, 1, 6, 8, 5, 3, 8, 0, 3, 1, 9, 0, 0, 8, 9, 7, 3, 5, 3, 2, 0, 4, 6, 0, 1, 8, 9, 6, 6, 9, 0, 2, 4, 1, 2, 2, 7, 6, 9, 5, 1, 7, 0, 9, 6, 2, 1, 8, 2, 7, 0, 5, 5, 6, 4, 6, 5, 3, 3, 5, 9, 7, 5, 5, 3, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the total area of all squares with sides parallel to the axes of the Cartesian coordinate system, the lower left vertex at (n,0) and the upper right vertex on f(x)=1/x for n=1..infinity. LINKS Martin Janecke, Edle Reihe FORMULA Sum_{n>=1} 1/[n;n,n,...]^2. Sum_{n>=1} 4/(n + sqrt(n^2 + 4))^2. EXAMPLE 0.9155879199018197251998168538031900897353... PROG (PARI) zeta(2)+sumpos(n=1, 4/(n+sqrt(n^2+4))^2-1/n^2) \\ Charles R Greathouse IV, Jan 26 2012 CROSSREFS Cf. A013661, A205325, continued fractions A001622, A014176, A098316, A098317, A098318. Sequence in context: A258268 A143296 A198355 * A021526 A019791 A006752 Adjacent sequences:  A205323 A205324 A205325 * A205327 A205328 A205329 KEYWORD cons,nonn AUTHOR Martin Janecke, Jan 26 2012 EXTENSIONS a(-5)-a(-86) from Charles R Greathouse IV, Jan 26 2012 STATUS approved

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Last modified June 26 14:05 EDT 2022. Contains 354884 sequences. (Running on oeis4.)