%I #23 Apr 29 2024 09:37:36

%S 1,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Decimal expansion of 3/2.

%C Sum of the inverses of the tetrahedral numbers (A000292). - _Michael B. Porter_, Nov 27 2017

%C For any triangle ABC, cos A + cos B + cos C <= 3/2; equality is obtained only when the triangle is equilateral (see the Kiran S. Kedlaya link). - _Bernard Schott_, Sep 17 2022

%H Kiran S. Kedlaya, <a href="https://igor-kortchemski.perso.math.cnrs.fr/olympiades/Cours/ineqs-080299.pdf">A < B</a>, (1999), Problem 6.2, p. 6.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%e 1.5000000000000000000000000000000000000000000000000000000000...

%o (PARI) 3/2. \\ _Charles R Greathouse IV_, Jan 10 2022

%Y Cf. A000292 (tetrahedral numbers).

%Y Sums of inverses: A002117 (cubes), A175577 (octahedral numbers), A295421 (dodecahedral numbers), A175578 (icosahedral numbers).

%Y Cf. A002194, A020821, A104956 (other trigonometric inequalities).

%K nonn,cons,easy

%O 1,2

%A _N. J. A. Sloane_, Oct 30 2009