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Help with this sum

  1. Jan 13, 2016 #1
    1. The problem statement, all variables and given/known data

    ∑n!/(3*4*5...*n)

    s1=1/3
    sn=1/3+2/(4*3)+3!/(5*4*3)+...+n!/(3*4*5*...n)


    so i multiplied the sum with 1/2sn=1/6+1/(4*3)+1/(5*4)+1/(6*5).....+1/((n+2)(n-1))

    got blocked here,i dont know how to continue, help please
     
  2. jcsd
  3. Jan 13, 2016 #2

    LCKurtz

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    What are the indices on the sum? The denominator makes no sense when n = 1. If the denominator had an additional factor of 2, what would you have?
     
  4. Jan 13, 2016 #3
    they are multiply symbols," * "=" x "
     
  5. Jan 13, 2016 #4

    LCKurtz

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    I knew that. But you didn't answer either of my questions. What is the range of the summation? What about n = 1? What about my last question?
     
  6. Jan 13, 2016 #5
    the range is infinite
    n=1 S1=1/3
    n=2 S2=1/3+2/12
    n=3 S3=1/3+2/12+3!/5*4*3
    .
    .
    .
    n=∞ Sn=1/3+2/12+3!/5*4*3...n!/(3*4*5*6*...*n)
     
  7. Jan 13, 2016 #6

    LCKurtz

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    You still aren't getting it. Your nth term is ##\frac{n!}{3\cdot4\cdot...\cdot n}##. That denominator is 3 times 4 times... up to n. It starts at 3 and works up to n. It makes no sense if n=1 or n=2 because you can't start at 3 and work up to 1 or 2.

    Also, you keep ignoring my last question. If there was a 2 in that denominator, how would it be different from the numerator? You can do some simplification.
     
  8. Jan 13, 2016 #7

    HallsofIvy

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    You appear to be copying things that you really do not understand. You say that the summand is [itex]\frac{n!}{3*4*\cdot\cdot\cdot n}[/itex] but that \certainly implies that n is at least 5: [itex]\frac{5!}{3*4*5}+ \frac{6!}{3*4*5*6}+ \cdot\cdot\cdot[/itex].

    Of course, n! means n(n-1)(n- 2)...(3)(2)(1) so that, for any n [itex]\frac{n!}{3*4*\cdot\cdot\cdot*n}= \frac{1*2*3*4\cdot\cdot\cdot n}{3*4*5\cdot\cdot\cdot n}= \frac{1}{2}[/itex] so, if I am interpreting this correctly this is just the sum [itex]\frac{1}{2}+ \frac{1}{2}+ \frac{1}{2}+ \cdot\cdot\cdot[/itex].
     
  9. Jan 13, 2016 #8

    LCKurtz

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    Or, you can just wait and HallsofIvy will simplify it for you.
     
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