A265303 - OEIS

A265303

Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).

8, 5, 7, 7, 2, 0, 6, 7, 6, 1, 3, 6, 1, 9, 1, 9, 6, 6, 0, 0, 4, 2, 2, 2, 7, 3, 5, 2, 2, 6, 5, 4, 4, 6, 1, 4, 4, 7, 9, 2, 0, 3, 5, 3, 0, 2, 5, 1, 2, 1, 6, 5, 4, 9, 3, 3, 6, 6, 0, 5, 9, 2, 0, 4, 4, 6, 1, 1, 3, 8, 6, 2, 7, 4, 1, 3, 3, 0, 7, 1, 7, 6, 5, 2, 2, 8

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

sum = 0.8577206761361919660042227352265446144...

MATHEMATICA

x = Sqrt[8]; z = 600; c = Convergents[x, z];

s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]

s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]

N[s1 + s2, 200]