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Question:

fairydrink
fairydrink
Student
High School - 10th Grade

Calculate lim S, where S=1/(1*2) + 1/(2*3) + ...+ 1/[n*(n+1)].

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Posted by fairydrink on Friday April 17, 2009 at 10:25 AM and tagged with limit, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Sn = 1/(2*3)+1/(3*4)++....1/(n*(n+1))

    =(1/2-1/3) +(1/3-1/4)+ (1/4-1/5)+....(1/n - 1/(n+1))

    =1/2 +(1/3-1/3)+1/4-1/4)+.....(1/n-1/n)-1/(n+1)

    =1/2+0+0...+0 -1/(n+1)

    =1/2 + 1/(n+1)

    Lim n->inf  Sn = 1/2 as 1/(n+1) approaches 0  as n becomes infinite.

     

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    Posted by neela on Wednesday May 27, 2009 at 8:52 PM