# Homework Help: Sum of a ? Series

1. Feb 28, 2010

### thyrsta

1. The problem statement, all variables and given/known data

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?

3. 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

2. Feb 28, 2010

### rock.freak667

For a minute let's make a quick substitution of x=lna

does the infinite sum of xn/n! look familiar?

3. Feb 28, 2010

### thyrsta

Sorry, no. I haven't learned much more beyond simple geometric and arithmetic series

4. Feb 28, 2010

### rock.freak667

Have you learned the Taylor/Maclaurin series of ex?

5. Feb 28, 2010

### thyrsta

No I haven't

6. Feb 28, 2010

### rock.freak667

In that case, without using the direct result of

$$e^x = \sum_{n=0} ^{\infty} \frac{x^n}{n!}$$

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

7. Feb 28, 2010

### thyrsta

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. Feb 28, 2010

### Dick

I don't think so. It's not a geometric series.

9. Feb 28, 2010

### thyrsta

Ok thanks a lot guys for your help