How to re-write this expression?

[kaffekjele]

Could someone please help me make this expression a little smaller? I'm sure there are things that cancels out or could be re written, but I generally suck at these things as I tend to break a few math rules along the way.
Could I for instance cancel n against n in the two last cosine expressions so I'm left with -cos∏-cos∏/2 at the end?

Expression is here: http://tinypic.com/r/2lw8047/6

 

[Ray Vickson]

Could someone please help me make this expression a little smaller? I'm sure there are things that cancels out or could be re written, but I generally suck at these things as I tend to break a few math rules along the way.
Could I for instance cancel n against n in the two last cosine expressions so I'm left with -cos∏-cos∏/2 at the end?

Expression is here: http://tinypic.com/r/2lw8047/6

Absolutely NOT! $\cos(n \pi)/n$ is most definitely not equal to $\cos(\pi).$ Just evaluate $\cos(n \pi)/n$ for $n = 2, 3, 4$ and see what you get.

Vital advice: put out of you mind forever any thought that you can cancel n's in such situations. Never try to cancel the n's in expressions like $\cos(nx)/n, \; \sin(nx)/n, \: e^{nx}/n, \; \log(nx)/n,$ etc. You just cannot do it.

 

[LCKurtz]

To add to what Ray said, you can give expressions for $\cos (n\pi)$ and $\cos(\frac{n\pi} 2)$ that don't involve cosines. Write them out for a few values of $n$ to see a pattern.

 

[SteamKing]

You must learn to think of sin, cos, etc. as functions.

If y(x) were defined as some function, I don't think you would say that

y(5n)/n was the same as y(5).