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Math Help - summation problem

  1. #1
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    Exclamation summation problem

    Find the sum.
    n
    E (2-5i) =
    i=1

    how would i do this?
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  2. #2
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    Generate the first few terms to see what's going on.
    Put in i=1, i=2, i=3,...
    The terms are -3, -8, -13, -18 etc. and you want to add these up.
    The numbers form an AP (arithmetic prgression) so find a and d, and use the sum of an AP formula.
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  3. #3
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    i think i get what your saying and i get n(-3-5)
    but its still wrong
    can u show me the steps and the solution to solve this
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  4. #4
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     \sum_{i = 1}^n 2 - 5i = \sum_{i = 1}^n 2 - 5 \sum_{i = 1}^n i = 2 - 5 \sum_{i = 1}^n i .

    Now use the formula for the sum of the first n positive integers.
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  5. #5
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    Formula for sum of AP is (n/2)(2a+(n-1)d)
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  6. #6
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    i am still very confused on how to do this question
    what is the a and d
    and how did u get (n/2)(2a+(n-1)d)
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  7. #7
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    Have you learnt about arithmetic progressions? If not check out JG89's suggestion. If you have learnt about APs the you should know the sum of a AP formula.
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  8. #8
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    ok now i get this question but now i have this question

    n
    E (i+1)(i+2)
    i=1

    the GP formula is

    a(1-r^n)
    ---------
    1-r

    what would a and r be
    a is the starting point so it would be 6 ?
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  9. #9
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    List a few terms first to get a feel for what you are looking at. Yes the first term is 6. list a few more. Is it a GP??
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  10. #10
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    ok i got that question now i dont know how to do this one

    100
    E (5^(i) - 5^(i-1))
    i=1
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  11. #11
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    (5^(i) - 5^(i-1)) = 5^(i) - 5^(i) x 5^(-1) = 5^(i)[ 1 - 5^(-1)]
    That should help.
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  12. #12
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    it helped and i got it right , i got 5^100 as the answer
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  13. #13
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sneaky View Post
    ok i got that question now i dont know how to do this one

    100
    E (5^(i) - 5^(i-1))
    i=1
    Do you know what a telescoping sum is?

    It means that all of the middle terms cancel leaving only a couple at the beggining and at the end. Think about your problem, which terms are gonna cancel other terms, and what are the only terms that will remain standing?
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  14. #14
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    I think the answer should be 5^100 minus 1.
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  15. #15
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Debsta View Post
    I think the answer should be 5^100 minus 1.
    And that would be correct!

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