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Summation Notation/Product

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Find Ʃ(product) with k=1 as the lower limit, and 50 as the upper limit. The formula is k/(k+2)


    2. Relevant equations



    3. The attempt at a solution
    I noticed a pattern where the first few numbers are:
    1/3, 2/4, 3/5, 4/6, 5/7 The denominator should cancel with the numerator of the next number in the pattern. I noticed this pattern for the odd numbered fractions. The last number in this odd numbered series will be 49/51, for which there are no cancellations possible, I think. For the even numbers, the pattern starts with 2/4 and ends with 50/52.

    I think the fraction left will be (1*2)/(51*52)= 1/(51*26)

    Is this logic right? I at first thought ..there is NO way they want me to multiply it out, and then realized there must be a pattern. So I tried and I hope I've got something. Thanks!
     
  2. jcsd
  3. Jun 13, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, right.
     
  4. Jun 13, 2013 #3
    Thank you very much! I appreciate it :)
     
  5. Jun 14, 2013 #4

    Mark44

    Staff: Mentor

    Your title is misleading, and your notation needs a little help. From your work, you aren't evaluating a sum, but a product. The notation for a product is a capital letter pi, or ##\Pi##.

    In LaTeX, the product would look like this:
    $$ \prod_{k = 1}^{50}\frac{k}{k+2}$$
    If you click the expression, you can see the LaTeX code that I wrote.

    Upper case sigma (Ʃ) is used for sums. ∏ is used for products.
     
  6. Jun 14, 2013 #5
    Thank you. I did look at the LaTeX code, and I do understand how it is to be written on paper, though I just did not know how to write it with the coding. Note taken. :P
     
  7. Jun 14, 2013 #6

    Mark44

    Staff: Mentor

    \prod_{k = 1}^{50}\frac{k}{k+2}
    This is the LaTeX code, which is written inside two pairs of $$ tags.
    \prod makes the capital pi.
    _ is used for subscripts or for the lower limit on integrals, sums, products, and so on.
    ^ is used for superscripts (exponents) or for the upper limit on integrals, sums, products, etc.
    \frac writes the things in braces as a fraction.
     
  8. Jun 14, 2013 #7
    Oh wow, thank you so much!
     
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