# Finding the Sum of an Infinite Series

1. Jun 25, 2014

### kq6up

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

Find the expectation value of the Energy the Old Fashioned way from example 2.2.

2. Relevant equations

$\left< E \right> =\frac { 480\hbar ^{ 2 } }{ \pi ^{ 4 }ma^{ 2 } } \sum _{ odds }^{ \infty }{ \frac { 1 }{ { n }^{ 4 } } }$

3. The attempt at a solution
Never mind the details of the physics problem. I am confident of those bits since it is from an example.

Using a symbolic math program, how to I only evaluate odds of a summation? I use sage and Wolfram Alpha normally. I tried using sin(pi*n/2)^2 to eliminate the even terms, but neither program seemed to take well to that.

Thanks,
Chris

2. Jun 25, 2014

### Zondrina

If I'm reading correctly you only want the sum of the odd terms. So make a change of index. Suppose that $n = 2k+1$. Then:

$\left< E \right> =\frac { 480\hbar ^{ 2 } }{ \pi ^{ 4 }ma^{ 2 } } \sum _{ k=0 }^{ \infty }{ \frac { 1 }{ { (2k+1) }^{ 4 } } }$

3. Jun 25, 2014

### kq6up

That might work. Let me give that a shot.

Chris

4. Jun 25, 2014

### kq6up

Perfect, thank you.

Chris