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Math Help - Sequences...

  1. #1
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    Sequences...

    it says...

    State whether the sequence converges and if it does, find the limit.

    sin[(pi)/(2n)]

    so do we do this..?

    lim (sin[(pi)/(2n)])
    n->oo

    but im stuck there. do we then do L'Hopital's rule?
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  2. #2
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    Quote Originally Posted by runner07 View Post
    do we then do L'Hopital's rule?
    Forget that.
    What is this limit?
    \lim _{n \to \infty } \left( {\frac{\pi }{{2n}}} \right)

    Now answer the question.
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  3. #3
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    the limit of that is 0 isnt it? so we just ignore the sine?
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  4. #4
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    Quote Originally Posted by runner07 View Post
    so we just ignore the sine?
    Absolutely not!.
    The sine function is continuous. Right?
    What is sin(0)?
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  5. #5
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    the sin(0) is 0....
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  6. #6
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    And that is the sequential limit.
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  7. #7
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    oh. does that work for all trig? like if its something like
    tan{[(n)(pi)] / (4n+1)}
    i would take the limit of pi(n)/ 4n+1... and i'd do L'Hopital's rule.... so it'd be lim pi/4.....??
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  8. #8
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    \left( {\frac{{n\pi }}{{4n + 1}}} \right) \to \frac{\pi }{4}\quad  \Rightarrow \quad \left[ {\tan \left( {\frac{{n\pi }}{{4n + 1}}} \right)} \right] \to \tan \left( {\frac{\pi }{4}} \right)
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