A205325 -id:A205325 - cp's OEIS frontend

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

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Martin Janecke, Jan 26 2012

cons
nonn

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.

			0.9155879199018197251998168538031900897353...

Martin Janecke, Edle Reihe

Cf. A013661, A205325, continued fractions A001622, A014176, A098316, A098317, A098318.

zeta(2)+sumpos(n=1,4/(n+sqrt(n^2+4))^2-1/n^2) \\ Charles R Greathouse IV, Jan 26 2012

Sum_{n>=1} 1/[n;n,n,...]^2.

Sum_{n>=1} 4/(n + sqrt(n^2 + 4))^2.

a(-5)-a(-86) from Charles R Greathouse IV, Jan 26 2012

cp's OEIS Frontend

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

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