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help with series question, convergent or divergent?
Show infinity series as n=1, cos(n)/n. Convergent or Divergent.
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- santmann2002Lv 71 decade agoFavorite Answer
There is a theorem due to Dirichlet
if an* bn is so that sum (1,n) an is bounded and bn==>0 monotonously
than sum an*bn converges
In this case bn= 1/n and an = cosn
and
Sum cos(n) =sin n/2* cos(n+1)/2/sin(1/2)
You can find the formula summing the geometric series Sum e^in=
sum(cosn +isin n) and taking the real part
Source(s): Theory and application of infinite series Dr.Konrad Knopp Blackie and Son Limited London and Glasgow
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