Simplify $(-1)^{n-1}\frac{800}{(\pi^2){(2n-1)^2}}$ Im having problems simplifying this equation, I know that the answer should be $$\frac{800}{(\pi^2)}\cdot \frac{(-1)^{n+1}}{(2n-1)^2}$$ however I'm not entirely sure why.. If someone could explain it would be a great help 
 A: It seems that there are two questions here:
The mathematical question 'why is $(-1)^{n-1}$ equal to $(-1)^{n+1}$?'
and the aesthetic question 'why is the expression with all constants (numbers) in one fraction on the left and all stuff that depends on $n$ together in another fraction on the right considered simpler than the original form?'
The mathematical question has been answered in the comments. As for the aesthetic question: of course this is subjective, but the form with constants separated from the rest helps see the structure. For instance in some computations you can help yourself by 'summarizing' the entire term $\frac{800}{\pi^2}$ as $C$ (or some other letter of your choice) so that it won't distract and initimidate you as much when you continue to do stuff with the rest of the equation. Another example of a context where the simplification would be useful: if this were one term in an infinite sum
$$\sum_{n=1}^\infty \frac{800}{\pi^2} \frac{(-1)^{n+1}}{(2n - 1)^2}$$ as suggested in the comments, then a next simplifying step could be to rewrite the entire sum as:
$$\frac{800}{\pi^2} \sum_{n=1}^\infty  \frac{(-1)^{n+1}}{(2n - 1)^2}$$
And this further simplification would be harder to see if you had not did the previous simplification (of changing the expression in the title to the one in the post).
