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Math Help - Writing the Sum Using Sigma Notation

  1. #1
    Newbie UnstoppableBeast's Avatar
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    Writing the Sum Using Sigma Notation

    Alright, it goes hand-in-hand with a previous topic titled "Summation Formulas" but yet...it's different at the same time.

    This time they give me two series:


    1. 1+1/2+2+5/2+...+6

    2. [1-(1/2)^2]+[1-(1/3)^2]+[1-(1/4)^2]+...


    My first reaction was that I would have to find the formula myself, where it starts, and where it ends. Simple...except not so much.

    The second one is possibly \sum_{n=1}^{INF}([1-(1/(1+N)^2]).

    Although that would be way to simple, hehe.
    The first one though, I can't seem to find a proper equation that fits the numbers given.
    Last edited by UnstoppableBeast; August 23rd 2011 at 01:44 PM.
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  2. #2
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    Re: Writing the Sum Using Sigma Notation

    The answer to the second one is correct.

    You could even say \displaystyle \sum_{n=2}^{\infty}1-\frac{1}{n^2}

    Can't see a pattern in the first one yet.
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  3. #3
    Newbie UnstoppableBeast's Avatar
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    Re: Writing the Sum Using Sigma Notation

    Yeah, I dunno what's going on with the first one. I spent at least an hour or two going over it but it's harder then it looks...and it looked pretty hard to start with.

    Oh, I also made a mistake on number one, accidently left out a number. Fixed it.

    Should be:


    1+\frac{1}{2}+2+\frac{5}{2}+...+6
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  4. #4
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    Re: Writing the Sum Using Sigma Notation

    Quote Originally Posted by UnstoppableBeast View Post
    Alright, it goes hand-in-hand with a previous topic titled "Summation Formulas" but yet...it's different at the same time.

    1. 1+{\color{red}1}/2+2+5/2+...+6
    I think it ought to be 1+\frac{{\color{blue}3}}{2}+2+\frac{5}{2}+\cdots+6.

    In which case it would be \sum\limits_{k =1}^{11} {\frac{{k + 1}}{2}}
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Writing the Sum Using Sigma Notation

    Is it possible the second term has to be \frac{3}{2} in stead of \frac{1}{2}?
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  6. #6
    Newbie UnstoppableBeast's Avatar
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    Re: Writing the Sum Using Sigma Notation

    Sadly no. It would've been easier that way but I'm sure of what the question is asking, I have the paper right in front of me.

    Maybe the person who made the packet made a mistake, seems as likely as anything.
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