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This might be more of a mathematical question than a physical one. But I am taking a Quantum Mechanics course and the book starts out by introducing the equation for the energy density of radiation from a black body. They then integrate this expression over infinity to find the total energy per unit volume.

http://img256.imageshack.us/img256/5189/blackbody.jpg [Broken]

My question is, how did they do the integral? It looks like they turned [itex]\frac{1}{e^{x}-1}[/itex] into its geometric series representation. That part I understand. But what do they do in the step after that? Where does the geometric series go? And where does the [itex]\frac{1}{(n+1)^4}[/itex] come from? And for that matter, the last line in the derivation?

I know its not an incredibly crucial question in understanding the Physics, but it bugs me a lot when I cannot follow the mathematics.

http://img256.imageshack.us/img256/5189/blackbody.jpg [Broken]

My question is, how did they do the integral? It looks like they turned [itex]\frac{1}{e^{x}-1}[/itex] into its geometric series representation. That part I understand. But what do they do in the step after that? Where does the geometric series go? And where does the [itex]\frac{1}{(n+1)^4}[/itex] come from? And for that matter, the last line in the derivation?

I know its not an incredibly crucial question in understanding the Physics, but it bugs me a lot when I cannot follow the mathematics.

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