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Math Help - sigma notations

  1. #1
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    Unhappy sigma notations

    Hey there people and fellow mathematicians,

    I need some help with the following:

    The question is as stated: "Write an expression in sigma notation as shown for suitable terms n_1,n_2 and a_i for each of these finite and infinite summations. i.e. \sum\limits_{i=n_1}^{n_2} a_i "

    S_2 = 1-3+5-...\pm(2n+1)

    Here's my solution:

    S_2 = \sum\limits_{n=0}^{n}(-1)^{n+2}(2n+1)

    Is this correct?

    Cheers
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by tsal15 View Post
    Hey there people and fellow mathematicians,

    I need some help with the following:

    The question is as stated: "Write an expression in sigma notation as shown for suitable terms n_1,n_2 and a_i for each of these finite and infinite summations. i.e. \sum\limits_{i=n_1}^{n_2} a_i "

    S_2 = 1-3+5-...\pm(2n+1)

    Here's my solution:

    S_2 = \sum\limits_{n=0}^{n}(-1)^{n+2}(2n+1)

    Is this correct?

    Cheers
    Yes! That's correct. However, in your notation, I would let the main variable be k, as in S_2 = \sum\limits_{k=0}^{n}(-1)^{k+2}(2k+1)

    Alternatively, \sum_{k=0}^{n}(-1)^k\left(2k+1\right) is correct as well.

    --Chris
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