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Help with sequence question

  1. Jul 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the general term of a sequence whose sum of the first n terms is S(n)=1/n(n+1)

    2. Relevant equations


    3. The attempt at a solution

    I am able to work out T(n) as through T(n)=S(n)-S(n-1)
    which works out to be -2/n(n-1)(n+1) however this doesn't work for when n=1

    Any help would be greatly appreciated :smile:
  2. jcsd
  3. Jul 18, 2007 #2
    expression you derived is from T(n)=S(n)-S(n-1) => T(1)=S(1)-S(0)
    T(1)=S(1) , S(0) doesn't make sense.

    T(1) can be directly calculated from general expression for S(n) for n=1
  4. Jul 18, 2007 #3


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    Staff Emeritus
    Science Advisor

    In other words, since a sum cannot have 0 terms, there is no such thing as S(0)! The first partial sum is S(1)= T(1).
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