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Math Help - Taking the Limit of Partial Sums

  1. #1
    Junior Member Coop's Avatar
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    Question Taking the Limit of Partial Sums

    Hi,

    It's been a while since I've practiced limits :s

    So I'm asked to find the limit of the sequence tan[4n*pi/(4+16n)]

    I take the limit of the things inside the brackets then I will look at what happens at tan(lim.)

    I break the fraction apart

    lim(n->inf) 4n*pi/4 + lim(n->inf) 4n*pi/16n = inf + pi/4

    Now, my question is, because one piece of the partial sum limit was infinity, does the whole thing inside the brackets go to infinity or pi/4? I thought it went to infinity, but I think my homework wants me to say it goes to pi/4 based on an example it gave.

    Any help? Thanks
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  2. #2
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    Re: Taking the Limit of Partial Sums

    Quote Originally Posted by Coop View Post
    So I'm asked to find the limit of the sequence tan[4n*pi/(4+16n)]

    You need to review of basic algebra.

    \frac{{4n\pi }}{{4 + 16n}} = \frac{\pi }{{\frac{1}{n} + 4}}
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  3. #3
    Junior Member Coop's Avatar
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    Re: Taking the Limit of Partial Sums

    Quote Originally Posted by Plato View Post
    You need to review of basic algebra.

    \frac{{4n\pi }}{{4 + 16n}} = \frac{\pi }{{\frac{1}{n} + 4}}
    Oh right, I don't even know why I thought I could break the fraction up like that, silly mistake.
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