# Homework Help: Question on summing

1. May 4, 2010

### c.dube

1. The problem statement, all variables and given/known data
Find the sum of the series:
$$\sum^{\infty}_{n=3}\frac{1}{(2n-3)(2n-1)}$$
2. Relevant equations
N/A
3. The attempt at a solution
This isn't geometric, I can't get it from any common Maclaurin series (as far as I can work out). The book I have tells me the answer is 1/6, I'm sure I'm doing something stupid. Thanks in advance for any help!

2. May 4, 2010

### Staff: Mentor

Try breaking up the summand using partial fraction decomposition, and then expand the series.

3. May 4, 2010

### c.dube

OK, so I have $$\sum^{\infty}_{n=3}\frac{1}{2(2n-3)}-\frac{1}{2(2n-1)}$$, but I'm not sure what you mean by "expanding the series"; should I split it into two summations? And if so, where do I go from there?

4. May 4, 2010

### Staff: Mentor

No, not two series - just one. Expanding the series means writing out the sum of terms, starting with the one for n = 3. Look at the sequence of partial sums, Sk, the sum of the terms from n = 3 to n = k.

5. May 4, 2010

### c.dube

*hits self in head* Wow! Thanks a ton, that should have been obvious.

6. May 4, 2010

### Staff: Mentor

These things are obvious only after you have done them a time or two.

7. May 4, 2010

### c.dube

Yah, well at least now when I see it again I'll know what to do! Thanks again for the help.