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Sum of a ? Series

  • Thread starter thyrsta
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  • #1
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Homework Statement



I have a question involving the sum of a series. I have already worked out a series, and the equation for a term in the series is:

((ln a)^n)/n!

a is just a variable, and n is the position in the sequence

a variation is:

(ln a)*((ln a)^(n-1))/n!

How would I start writing an equation for the sum of the series?




The Attempt at a Solution


I tried using the variation and treating it as a geometric series, with (ln a) as the first term, but that didn't work, for obvious reasons, since the second part isn't exactly the difference/scalar
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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Homework Statement



I have a question involving the sum of a series. I have already worked out a series, and the equation for a term in the series is:

((ln a)^n)/n!

a is just a variable, and n is the position in the sequence

a variation is:

(ln a)*((ln a)^(n-1))/n!

How would I start writing an equation for the sum of the series?




The Attempt at a Solution


I tried using the variation and treating it as a geometric series, with (ln a) as the first term, but that didn't work, for obvious reasons, since the second part isn't exactly the difference/scalar
For a minute let's make a quick substitution of x=lna

does the infinite sum of xn/n! look familiar?
 
  • #3
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For a minute let's make a quick substitution of x=lna

does the infinite sum of xn/n! look familiar?
Sorry, no. I haven't learned much more beyond simple geometric and arithmetic series
 
  • #4
rock.freak667
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Sorry, no. I haven't learned much more beyond simple geometric and arithmetic series
Have you learned the Taylor/Maclaurin series of ex?
 
  • #5
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Have you learned the Taylor/Maclaurin series of ex?
No I haven't
 
  • #6
rock.freak667
Homework Helper
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No I haven't
In that case, without using the direct result of


[tex]e^x = \sum_{n=0} ^{\infty} \frac{x^n}{n!}[/tex]


I am not sure how to get you a closed for solution.
 
  • #7
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In that case, without using the direct result of


[tex]e^x = \sum_{n=0} ^{\infty} \frac{x^n}{n!}[/tex]


I am not sure how to get you a closed for solution.
so eln a=a

But is there any way to have an equation that would give you the sum of a given number of terms in the series?
 
  • #8
Dick
Science Advisor
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so eln a=a

But is there any way to have an equation that would give you the sum of a given number of terms in the series?
I don't think so. It's not a geometric series.
 
  • #9
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I don't think so. It's not a geometric series.
Ok thanks a lot guys for your help
 

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