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A233383 Decimal expansion of the absolute value of sum_{n>=1} (-1)^n*sin(1/n). 0
5, 5, 0, 7, 9, 6, 8, 4, 8, 1, 3, 3, 9, 2, 9, 4, 7, 5, 5, 1, 0, 0, 6, 6, 9, 5, 7, 4, 3, 5, 1, 1, 8, 4, 1, 4, 3, 9, 6, 1, 7, 6, 8, 0, 8, 9, 0, 0, 5, 3, 7, 6, 6, 5, 7, 1, 5, 8, 8, 6, 9, 6, 8, 7, 6, 6, 1, 8, 3, 1, 0, 6, 2, 9, 0, 8, 6, 3, 0, 4, 5, 6, 2, 1, 2, 0, 2, 4, 6, 8, 1, 4, 6, 4, 4, 9, 5, 0, 0, 3, 9, 9, 7, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If the contribution of the first term, -sin(1) = -A049469, is omitted, the constant becomes sum_{n>=1} [ sin(1/(2n)) - sin(1/(2n+1)) ] = 0.29067413667396703114243536419518058522...

LINKS

Table of n, a(n) for n=0..104.

oldrinb, Evaluating the infinite series sum_n=1^infty [sin(1/2n)-sin(1/(2n+1))], math.stackexchange, Aug 22 2013

EXAMPLE

Equals 0.550796848133929475510066957...

MAPLE

M := 141 :

Digits := 120 :

s := sin(1/2/n)-sin(1/(2*n+1)) :

add(subs(n=i, s), i=1..M) :

pre := evalf(%) :

zetaM := proc(s, M)

    local n ;

    Zeta(s)-add(1/n^s, n=1..M) ;

    evalf(%) ;

end proc:

for dd from 75 to 90 by 5 do

    subs(n=1/eps, s) ;

    taylor(%, eps=0, dd+1) ;

    t := gfun[seriestolist](%, 'ogf') ;

    add( op(j, t)*zetaM(j-1, M), j=3..nops(t)) ;

    x := pre+% ;

    print(x) ;

end do:

# now sum_{n>=1} (-1)^n*sin(1/n) = -0.5570986.

x-sin(1.0) ;

MATHEMATICA

digits = 105; NSum[(-1)^n*Sin[1/n], {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+10] // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Feb 24 2014 *)

CROSSREFS

Sequence in context: A200257 A236023 A200516 * A144184 A119380 A121212

Adjacent sequences:  A233380 A233381 A233382 * A233384 A233385 A233386

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Dec 08 2013

STATUS

approved

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)