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What is limit in sequence a(subscript n)=nln(1+sin(3pie)/2n)?

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greenbel | Honors

Posted August 20, 2013 at 2:24 PM via web

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What is limit in sequence a(subscript n)=nln(1+sin(3pie)/2n)?

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aruv | High School Teacher | Valedictorian

Posted August 20, 2013 at 2:52 PM (Answer #1)

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`a_n=nxxln(1+sin((3pi)/(2n)))`

`a_n=nxx(sin((3pi)/(2n))-(sin((3pi)/(2n)))^2/2+....)`

`|sin((3pi)/(2n))|<=1`

`|nsin((3pi)/(2n))|<=n`

`|a_n|<=|nsin((3pi)/(2n))|<=n`

`lim_(n->oo)|a_n|<=lim_(n->oo)(n)`

`Thus`

`lim_(n->oo)a_n =oo`

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