DivineNathicana Posted December 6, 2004 Report Posted December 6, 2004 Greetings. Alright, if anyone's bored enough to be on-line right now, what is the following simplified and how do you get it? (1-1/2)(1-1/3)(1-1/4)(1-1/5)...(1-1/n) Thanks for any help, - Alisa
Bo Posted December 6, 2004 Report Posted December 6, 2004 the answer is 1/n, and it can be obtained as follows: rewrite your equation as:(1/2)*(2/3)*(3/4)*...*((n-2)/(n-1))*((n-1)/n) if you look at the last term, you see that the two (n-1) terms cancel each other. It can be easily seen that this works for all terms, except the first 1 and the last n, so your left with 1/n Bo
DivineNathicana Posted December 7, 2004 Author Report Posted December 7, 2004 Yeah, thanks Bo. I was doing this yesterday (or rather today) around 2 A.M. in the morning, so the thinking was pretty slow, but I got it right! Yay! hahaha Thanks again, - Alisa
Bo Posted December 7, 2004 Report Posted December 7, 2004 no problem, just doing my job :wink: What did you need the result for? Bo
DivineNathicana Posted December 8, 2004 Author Report Posted December 8, 2004 An arbitrary assignment from my rather odd math teacher required that I do it... And granted, I forgot about it until around 2 A.M. (go me!), when my thinking cap was long-retired. = ) - Alisa
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