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Math Help - arithmetic series or sequences...

  1. #1
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    Angry arithmetic series or sequences...

    i need help with two questions...

    1. find the suma of all the intergers between 1 and 200 that are not multiples of 7.


    and i have just realised that i have no idea how to do sigma questions on herebut i'll try to describe it.

    2. find (at the bottom of the sigma sign r=1 and at the top of it n then next to it 1-(r/3)), giving your answer in the form (n/a)(b-n), where a and b and intergers.


    thanks for any help

    if you cant understand 2. ask me and i'll help you
    thanks again
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  2. #2
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    #1: The sum of the first 200 integers excluding the multiples of 7 (i.e. from 7, 14, 21, ..., to 196) is equal to the total sum of the first 200 integers minus the sum of the multiples of 7:
    \underbrace{\sum_{n=1}^{200} n}_{\text{Sum of 1 to 200}} \ - \ \underbrace{\sum_{n=1}^{28} 7n}_{\text{Sum of 7 + 14 + 21 + ... + 196}}

    #2: Use your summation properties:
    \sum_{r = 1}^{n} \left(1 - \frac{r}{3}\right)\ \  = \ \ \sum_{r=1}^{n} 1 - \sum_{r=1}^{n} \frac{r}{3}\  \ = \ \ \sum_{r=1}^{n} 1 - \frac{1}{3}\sum_{r=1}^{n} r \ \ = \ \ \hdots
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  3. #3
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    ok i get #1 but i'm still not with #2 could you please explain ti a bit more

    thanks
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  4. #4
    o_O
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    What don't you understand?

    You should know these: \sum_{i=1}^{n}1 = \underbrace{1 + 1 + \hdots + 1}_{n \text{ times}} = n....... \sum_{i=1}^{n} i = 1 + 2 + 3 + \hdots + n = \frac{n(n+1)}{2}

    Just a matter of simplifying after you substitute those in.
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  5. #5
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    Smile

    ok i get it now must have read it wrong before thanks for explaining ti again though
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