Mathematical clumsiness?

No.11913339 ViewReplyOriginalReport
Hey sci. I like to give myself interesting math problems to solve when I'm bored at work. The problem I have is my methodology for solving such problems. They're often contrived, silly, and would make any self respecting mathematician worth his salt get a chuckle out of me. Pic related is an expression I made to solve a problem were I must find the arithmetic mean of the first n odd numbers but on the condition that every 2nd odd number is skipped. This expression works, but I don't exactly understand the reasoning behind the 4 and 2 other than that it helps add the first and last number. Can any of you guys provide a more efficient and smarter way of solving this problem? If you have alternative equations, that would be cool too.