How can I describe the pattern of the sequence: 1,0,-1,0,1,0,-1,0 starting at n=1?

[bizztheizz]

So lets say I have a series starting at n=1 of sin(n*(pi/2)). This would create the sum 1+0+(-1)+0+..... and so on. How can I describe this with the form A(-1)^(Bn+C) + D or similar. Like how the sum starting at n=1 cos(n*pi) would be the sum (-1)+1+(-1)+1+......

I apologize for my straining for a better way to describe this problem but I am curious if there is a solution. If you have questions about what Im asking please ask them below and I hope I can be more clear on what I am asking.

 

[Dr.Peterson]

A piecewise function (0 for even i, (-1)^i for odd i) is perfectly acceptable for most purposes. The sine version is more cumbersome (as it answers a problem about integers in terms of irrational numbers) but still valid. It could also be written in terms of complex numbers, but that's going even further afield.

There is no particular virtue in writing it as a single algebraic formula. Often when you can do so, with some effort, the result is far harder to work with than the piecewise form.

Is your question entirely a matter of curiosity, or is there some purpose for the form you are hoping for?