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Calculating the number of terms in sequences

  1. Nov 13, 2013 #1
    How does one calculate the number of terms in the sequence

    \sum\limits_{a=2}^k \sum\limits_{b=a}^k of 1/(a*b).
     
  2. jcsd
  3. Nov 13, 2013 #2

    Mark44

    Staff: Mentor

    Is this what you're asking about?

    $$ \sum_{a = 2}^k \sum_{b = a}^k \frac 1 {ab}$$

    In any case, this is not a sequence, it's a sum (a double summation). To find how many terms, start by expanding the inner sum, and than expand the outer sum.
     
  4. Nov 14, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The "ath" term has k- a+ 1= k+1- a terms so there are [tex]\sum_{a= 2}^k (k+ 1- a)[/tex] We can write that as [tex]\sum_{a= 2}^k (k+1)- \sum_{a= 2}^k a[/tex]. Of course, [tex]\sum{a= 2}^k (k+1)= (k-1)(k+1)[/tex]. What is [tex]\sum_{a=2}^k a[/tex]?
     
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