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Math Help - Geometric/Arithmatic Series

  1. #1
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    Geometric/Arithmatic Series

    a)Using the appropriate formula, calculate:
    9
    Σ
    (2)n5n

    n
    =1


    b) A company is considering sending a team of divers, with all the appropriate equipment, down to a famous German U
    boat wreck. It will cost $560 for the first metre, $640 for the second metre, $720 for the third metre, and so on increasing $80 each time. Using the appropriate formula, determine how much it will cost to reach the Uboat, which is at a depth of 85 metres?

    c) Given that a wealthy historian is willing to pay the company $1,000,000 for any artefacts collected from the U
    boat in b), what will be the profit (loss) to the company if they go ahead with the dive?


    The answers I got were:
    a) -909090910
    b) $333,200
    c) $668,800

    Did I go wrong? Thanks

    Ibrox

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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Is a?
    \sum_{i=1}^{n}\{(-2)^n 5n\}

    its quite unclear
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  3. #3
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    Hello, ibrox!

    I assume those tiny numbers are exponents.


    Using the appropriate formula, calculate: . \sum^9_{n=1}(\text{-}2)^n\cdot5^n
    Your answer is correct! . . . Good work!


    We have: . \sum^9_{n=1}(\text{-}10)^n

    This is a geometric series with first term a = \text{-}10,
    . . common ratio r = \text{-}10, and n = 9 terms.

    The sum is: . S \;=\;a\,\frac{1-r^n}{1-r} \;=\;<br />
(\text{-}10)\,\frac{1-(\text{-}10)^9}{1 - (\text{-}10)} \;=\;(\text{-}10)\,\frac{1-(\text{-}1,\!000,\!000,\!000)}{11}

    . . . . . . . . . . . = \;(\text{-}10)\,\frac{1,\!000,\!000,\!001}{11} \;=\;(\text{-}10)(90,\!909,\!091) \;=\;\boxed{-909,\!090,\!910}

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  4. #4
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    Yes, that's what I meant...hard to use that program so I had to copy/paste. Thanks guys.
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