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Sum to infintiy

  1. Jan 10, 2005 #1
    1+(1/2)+(1/3)+(1/4)+(1/5).........+(1/n)

    can sum one prove this series is divergent????????



    or just tell me what the expression for sum to infintiy in terms of n is????????
     
  2. jcsd
  3. Jan 10, 2005 #2

    matt grime

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    replace with a strictly smaller divergent series eg 1+1/2+1/4+1/4+1/8+1/8+1/8+1/8+1/16... or use the integral test.
     
  4. Jan 10, 2005 #3
    but i thot that the integral test is not valid for series coz the graph of 1/n will not be contiuous :eek:
     
  5. Jan 10, 2005 #4

    matt grime

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    I think you ought to look up the integral test and see what it says. The integral test is a perfectly valid way to prove this result.
     
  6. Jan 10, 2005 #5
    Forget the first term (1), and observe that:

    1/2+1/3 + 1/4+1/5+1/6+1/7 + 1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15 +...>

    2*1/4 + 4*1/8 + 8*1/16 +.... =

    1/2 + 1/2 + 1/2 +...


    Is it enough ?
     
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