The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A342647 Decimal expansion of Sum_{n>=1} log(cos(1/n)) * log(sin(1/n)). 0
 5, 8, 8, 2, 5, 1, 4, 3, 3, 9, 6, 8, 1, 6, 3, 5, 6, 4, 7, 4, 1, 7, 8, 3, 1, 1, 7, 9, 4, 2, 5, 3, 1, 4, 3, 7, 2, 2, 8, 4, 7, 5, 7, 2, 7, 7, 6, 2, 5, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS log(cos(1/n)) ~ -1/(2*n^2) when n -> oo, so the series log(cos(1/n)) is convergent (A336603), but log(sin(1/n)) ~ -log(n) when n -> oo, so the series log(sin(1/n)) is divergent. However, as log(cos(1/n)) * log(sin(1/n)) ~ log(n)/(2*n^2) when n -> oo, the series log(cos(1/n)) * log(sin(1/n)) is convergent. REFERENCES Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.f p. 279. LINKS Table of n, a(n) for n=0..50. FORMULA Equals Sum_{n>=1} log(cos(1/n)) * log(sin(1/n)). EXAMPLE 0.588251433968163564741783117942531437228475727762559... PROG (PARI) sumpos(n=1, log(cos(1/n)) * log(sin(1/n))) \\ Michel Marcus, Mar 18 2021 CROSSREFS Cf. A336405, A336603. Sequence in context: A231786 A007450 A303816 * A200297 A155735 A153611 Adjacent sequences: A342644 A342645 A342646 * A342648 A342649 A342650 KEYWORD nonn,cons,more AUTHOR Bernard Schott, Mar 17 2021 EXTENSIONS a(4)-a(51) from Jon E. Schoenfield, Mar 18 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 15 13:23 EDT 2024. Contains 375938 sequences. (Running on oeis4.)