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Originally Posted by Stompy
At least with other problems like hydrostatic pressure or finding the area between two polar equations has a definite method to em. These seem more or less hit and miss... either you're lucky to find the answer, or you're not. IMO, not something you should be graded on.
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Um, ok. Math is not supposed to be about memorizing methods. That's what you have engineering courses are for. Given your complaint about spending 20 minutes on a problem, I guess you've only been given mechanical problems.
Anyways, I'll try to give you some idea of how to come up with these things on your own. If you have a sequence with an alternating pattern, (-1)^n is your friend (this is the same as cos(n pi)). Notice that (1+(-1)^n)/2={0,1,0,1,...}. This is very useful if you have one sequence nested in another.
You could therefore write your series as 1*(1+(-1)^n)/2+5*(1+(-1)^(n+1))/2. This simplifies to 3-2(-1)^n. You could also have come up with this directly by noting that 5 and 1 are equivalently 3+/-2.
For a more complicated example, take {1,4,3,16,5,36,...}. The odd terms are given by n, and the even terms by n^2. One way to write the general term is n*(1+(-1)^(n+1))/2 + n^2*(1+(-1)^n)/2. Of course this can be simplified and written in different ways, but the point is that you can separate out the even and odd terms very easily.
Also, if I were your prof, I wouldn't mark you off for using conditionals. It's easier that way. I'm not guaranteeing that he'll be the same though!