Club409
The best damn waste of time!
Research on Circles Leads to Tangents
mike
Total posts: 2298
6/22/2006 5:32 PM
I think the time I spend trying to research plasma is defined by 
mwinter
Total posts: 4327
6/23/2006 6:38 AM
:roflcopter:
Drew
Total posts: 5115
6/23/2006 10:39 AM
The time I spent in philosophy class listening to other people talk was definitely
mike
Total posts: 2298
6/23/2006 9:46 PM
:') my first roflcopter ever
mwinter
Total posts: 4327
8/3/2009 6:34 AM
Can someone explain this because it still doesn't make sense
SmoovB
Total posts: 1097
8/3/2009 12:33 PM
I know there are a few ways to solve this. I don't know if I'm forgetting something essential or breaking some rules:
By induction you can show that (x^n - 1) = (x-1)*(x^(n-1) + x^(n-2) + ... + 1)
(1 - x^n)/(1-x) = sum(x^k) for (x = 1:n-1)
lim n->inf ( (1 - x^n)/(1-x)) = 1/(1-x) for all x < 1
1/(1-x) = sum(x^k) for (x = 1:inf)
By induction you can show that (x^n - 1) = (x-1)*(x^(n-1) + x^(n-2) + ... + 1)
(1 - x^n)/(1-x) = sum(x^k) for (x = 1:n-1)
lim n->inf ( (1 - x^n)/(1-x)) = 1/(1-x) for all x < 1
1/(1-x) = sum(x^k) for (x = 1:inf)
Steven
Total posts: 751
8/4/2009 4:12 AM
your derivation is correct but the key is the second to last step. when you take the limit as n->inf of ((1 - x^n)/(1-x)) you get 1/(1-x) ONLY IF |x|<1. otherwise lim{n->inf} (1-x^n)/(1-x) is infinite and the final line is not valid. basically what that guy did is assume that the final equation (which should only be valid for |x|<1) is valid for any x. technically you get a number when you plug in x=2 but it bears no relation to the infinite sum because you've violated the conditions required to get the formula. he's proposing that there is some hidden meaning to the formula which is still valid for |x|>1 but it's just nonsense.
he supports the hidden meaning by saying the the sum is in fact equal to -1 if you use the p-adic valuation but that is even more nonsense. its comparable to performing a calculation in base 10 and then saying that the result has significant meaning in base 2. and his p-adic argument only holds for x=2 (if there was deeper meaning to the formula shouldn't it be valid for more than just a single value?)
basically this guy is only one step above the nullity guy in my book. he's only better because he hasn't claimed that his sketchy math allows him to solve problems that nobody has ever solved before
he supports the hidden meaning by saying the the sum is in fact equal to -1 if you use the p-adic valuation but that is even more nonsense. its comparable to performing a calculation in base 10 and then saying that the result has significant meaning in base 2. and his p-adic argument only holds for x=2 (if there was deeper meaning to the formula shouldn't it be valid for more than just a single value?)
basically this guy is only one step above the nullity guy in my book. he's only better because he hasn't claimed that his sketchy math allows him to solve problems that nobody has ever solved before
mwinter
Total posts: 4327
8/4/2009 4:34 AM
Ok i'm glad someone else thought it was poppycock
SmoovB
Total posts: 1097
8/5/2009 3:59 PM
yeah I missed the "abs" operator.