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Series and Sigma Notation

  1. Jan 8, 2005 #1

    Mo

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    Series and "Sigma" Notation

    I have been revising over the sigma/sequences and series chapters, this is the second question now where i have had different answers to the book - yet- my answers seem to work - i think....

    The question :

    Write in [tex]\sum[/tex] notation

    1 - 2 + 4 - 8 + 16 - 32


    My answer is:

    [tex]\sum_{0}^5 -2^r[/tex]

    Is this correct?

    Thie answer in the book by the way is:

    [tex]\sum_{1}^6 (-1)^{r+1} \ 2r^{r-1}[/tex]

    Regards,
    Mo
     
  2. jcsd
  3. Jan 8, 2005 #2
    Nope. Every term in that sum is negative (which is not true for 1 - 2 + 4...).
     
  4. Jan 8, 2005 #3

    dextercioby

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    Science Advisor
    Homework Helper

    Then the answer in the books seems wrong and yours as well.
    [tex] 1-2+4-8+16-32=(-)^{0}2^{0}+(-)^{1}2^{1}+(-)^{2}2^{2}+(-)^{3}2^{3}+(-)^{4}2^{4}+(-)^{5}2^{5}=\sum_{k=0}^{5}(-)^{k}2^{k} [/tex]

    You might have mistyped the answer in the book.

    Daniel.
     
  5. Jan 8, 2005 #4

    Mo

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    Yes i have typed in ther answer from the book wrongly, very sorry about that.

    [tex]\sum_{1}^6 (-1)^{r+1} \ 2^{r-1}[/tex]

    is the correct one.

    However i still can't see how my answer is wrong!

    when r is 0 , the answer is +1
    when r is 1 , the answer is -2
    when r is 2 , the answer is +4
    when r is 3 , the answer is -8

    so this would mean +1-2+4-8 ? Or maybe im making a really stupid mistake here!

    Thanks for your replies so far!
     
  6. Jan 8, 2005 #5
    At first, I thought your answer was right. It's not, cos your sum is -2^r and not (-2)^r. When r is 0, for your answer, you get -1, ie. -1 x 2^0.
     
  7. Jan 8, 2005 #6
    Your answer would have been correct if you would have used this one: -

    The following code was used to generate this LaTeX image:



    [tex] \sum_{k=0}^{5}(-2)^{k} [/tex]
     
  8. Jan 8, 2005 #7

    jtbell

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    Staff: Mentor

    Look at it this way: If you had

    [tex]\sum (1-2^r)[/tex]

    would you say that was

    [tex](1-1) + (1-2) + (1-4) + ...[/tex]

    or

    [tex](1+1) + (1-2) + (1+4) + ...[/tex]

    ?

    When you evaluate an expression that doesn't have parentheses inside of it, and is on a single line, exponents always come first, then multiplication/division, then addition/subtraction.
     
  9. Jan 8, 2005 #8

    Mo

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    Thank you for your replies all

    Offcourse i should have used brackets :sigh: next time ill remember!

    thanks again

    Regards,
    Mo

    PS: JTbell, this first one ..
     
  10. Jan 8, 2005 #9

    jtbell

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    Staff: Mentor

    I just realized that I got the signs backwards on my second choice. :yuck:

    Oh well, you got the right idea, anyway!
     
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