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How calculate a(subscript n) and limit of sequence a(subscript n) if a(subscript...

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ruals | Salutatorian

Posted September 25, 2013 at 10:41 AM via web

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How calculate a(subscript n) and limit of sequence a(subscript n) if a(subscript n)=(1/pi(4n-4-2b(subscript n)))^n and b(subscript n)=int_1^n 2x^2/(x^2+1)dx?

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aruv | High School Teacher | Valedictorian

Posted September 25, 2013 at 11:04 AM (Answer #1)

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`b_n=int_1^n(2x^2)/(x^2+1)dx`

`=2int_1^n(x^2+1-1)/(x^2+1)dx`

`=2{int_1^ndx-int_1^n1/(1+x^2)dx}`

`=2((n-1)-(tan^(-1)(n)-pi/4))`

`a_n=1/(pi(4n-4-2b_n))^n`

`=1/(pi(4n-4-4n+4+4(tan^(-1)(n)-pi/4)))^n`

`=1/(pi(4tan^(-1)(n)-pi))^n`

What limit ? It is not given in question. I have calculated `b_n and a_n .`

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