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Math Help - Sequences

  1. #1
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    Post Sequences

    1) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV".







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    Last edited by nhatie; April 28th 2010 at 09:46 PM.
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  2. #2
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    Quote Originally Posted by nhatie View Post
    1) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV".
    As the first part obviously goes to zero convergence is determined by the second part: 4 \arctan(n^2)

    What happens to \arctan(x) as x \to \infty ?

    CB
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  3. #3
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    will it be pi/2?
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    Quote Originally Posted by nhatie View Post

    2) Daniel and Alice want to purchase a house. Suppose they invest dollars per month into a mutual fund. How much will they have for a downpayment after years if the per annum rate of return of the mutual fund is assumed to be percent compounded monthly?




    The monthly rate of interest is 9.5/12 \% so now just write out the series representing the amount after 60 months.

    Hint:
    the first months payments will after 60 months be worth:  600(1+9.5/1200)^{60} dollars,
    and the second months payment will be worth:  600(1+9.5/1200)^{59} dollars

    etc.

    This will give you a geometric series which you will need to sum.

    CB
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    Quote Originally Posted by nhatie View Post
    will it be pi/2?
    Yes

    CB
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    Yes

    CB
    so is it a final answer? Because they said it was wrong!
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    The monthly rate of interest is 9.5/12 \% so now just write out the series representing the amount after 60 months.

    Hint:
    the first months payments will after 60 months be worth:  600(1+9.5/1200)^{60} dollars,
    and the second months payment will be worth:  600(1+9.5/1200)^{59} dollars

    etc.

    This will give you a geometric series which you will need to sum.

    CB
    thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
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  8. #8
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    Quote Originally Posted by nhatie View Post
    thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
    Sorry, the limit of \arctan(n^2) is \pi/2, you are effectivly asked for the limit of 4\arctan(n^2) which is 2\pi.

    CB
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  9. #9
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    Quote Originally Posted by nhatie View Post
    thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
    i got 46216.29: is it rite??
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  10. #10
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    Quote Originally Posted by nhatie View Post
    i got 46216.29: is it rite??
    Yes (I have 46816.35)

    CB
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  11. #11
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    Quote Originally Posted by nhatie View Post
    thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
    As I said its a finite geometric series, you can use the formula for the sum of such a series.

    CB
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