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Math Help - Summation Series... How to solve?? Plz help...

  1. #1
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    Summation Series... How to solve?? Plz help...

    May I know how to expand this??

    Given that
    x=2,
    y=3,
    Lambda1 = 1.5
    Lambda2 = 1.0
    Lambda3 = 0.05

    What's the answer?
    Thanx in advance
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  2. #2
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    Hello, phishboane!

    It seems to be simple substitution . . . then arithmetic.


    Given that: . x=2,\;y=3, \; \lambda_1 = 1.5,\;\lambda_22 = 1.0,\;\lambda_3 = 0.05

    Evaluate: . \sum^{\min(x,y)}_{i=0} {x\choose i}{y\choose i}(i!)\left(\frac{\lambda_3}{\lambda_1\lambda_2}\r  ight)^i

    We see that: . \min(x,y) \:=\:\min(2,3) \:=\:2

    . . and: . \frac{\lambda_3}{\lambda_1\lambda_2} \:=\:\frac{0.05}{(1.5)(1.0)} \:=\:\frac{1}{30}


    And we have: . \sum^2_{i=0}{2\choose i}{3\choose i}(i!)\left(\frac{1}{30}\right)^i

    . . = \;{2\choose0}{3\choose0}(0!)\left(\frac{1}{30}\rig  ht)^0 + {2\choose1}{3\choose1}(1!)\left(\frac{1}{30}\right  )^1 + {2\choose2}{3\choose2}(2!)\left(\frac{1}{30}\right  )^2

    . . = \;1\cdot1\cdot1\cdot1 \;+\; 2\cdot3\cdot1\cdot\frac{1}{30} \;+ \;1\cdot3\cdot2\cdot\frac{1}{30^2}

    . . = \;1 + \frac{1}{5} + \frac{1}{150}

    . . = \;\frac{181}{150}

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  3. #3
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    Sep 2008
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    Thanx Soroban.

    Hi Soroban,

    By looking at ur reply, ur solution steps. I know that I've made a correct decision to join this forum, n perhaps, I should have join earlier.
    I appreciate ur kind approach, n ur detailed solutions. Thanx a lot.
    The way u solved it was exactly the way i tried before but didn't get it right. So I think, the min(x,y) not as easy as we thought...
    Do u have some other solutions?
    Im really glad that u've replied my thread. TQ very much n nice to know u.
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