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Math Help - Don't understand this summation problem

  1. #1
    Senior Member Mukilab's Avatar
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    Don't understand this summation problem

    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}n}  = {\left( { - 1} \right)^{n + 1}}n

    and


    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}}  = {\left( { - 1} \right)^{n }}
    ^Thanks to Plato for the Latex code

    I just don't understand how to do these kind of things with a different letter on top. I know that I have to do something such as (-1)^1 + (-1)^2 + ... + (-1)^{2k} for the second one but then how do you solve that?

    Do I just ignore all the iterations until k? For example in the second one should I only look at (-1)^{2k}*2k? If so, shouldn't the answer be -2k since the first part will give you negative 1?

    Sorry for the failed latex. I looked at the latex crash course but I still managed to screw everything up. Please can someone clean up my latex so I can at least understand how to use it properly?
    Last edited by Mukilab; September 8th 2012 at 02:20 PM.
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  2. #2
    Super Member girdav's Avatar
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    Re: Don't understand this summation problem

    Could you write the indexes of the sums? Thanks!
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  3. #3
    Senior Member Mukilab's Avatar
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    Re: Don't understand this summation problem

    Sorry, the top of the first one is 2k, the bottom is n=1.

    Next to it is (-1)^(n+1) *n


    The second one has the same top and bottom but next to it (on the right) is (-1)^n
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  4. #4
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    Re: Don't understand this summation problem

    Quote Originally Posted by Mukilab View Post
    Sorry, the top of the first one is 2k, the bottom is n=1. Next to it is (-1)^(n+1) *n

    The second one has the same top and bottom but next to it (on the right) is (-1)^n
    Are these they?
    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}n}  = {\left( { - 1} \right)^{n + 1}}n

    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}}  = {\left( { - 1} \right)^{n }}?

    You can click on "reply with quote" to see the LaTeX code.
    Thanks from Mukilab
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  5. #5
    Senior Member Mukilab's Avatar
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    Re: Don't understand this summation problem

    Quote Originally Posted by Plato View Post
    Are these they?
    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}n}  = {\left( { - 1} \right)^{n + 1}}n

    \sum\limits_{n = 1}^{2k} {{{\left( { - 1} \right)}^{n + 1}}}  = {\left( { - 1} \right)^{n }}?

    You can click on "reply with quote" to see the LaTeX code.
    Yes! Thank you very much, updated my OP.

    Still waiting for an answer or help though
    Last edited by Mukilab; September 9th 2012 at 12:23 AM.
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