A205326 Decimal expansion of the sum of [0;n,n,n,...]^2 for n=1..infinity.

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

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

Table of n, a(n) for n=0..86.

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