Originally posted by humyEdit: posted in reply to a post that was later edited to say he understood it...this is a little redundant now.
Although I don't understand that proof ( "-1/x"? cannot see how that relates but I bet I am being completely stupid here ), I greatly appreciate your insight. "K/x^2" somehow intuitively looks about right to me even if I can't see why.
Originally posted by humyArr, after not getting it for ages, I suddenly got it just literally only one min after I posted this!
I normally am good at basic algebra. But, while working on something, I accidentally found that:
( x/(x + 1) ) – ( x/(x + 2) ) = x/( (x + 1)(x + 2) )
and I cannot see why the above is true with the simple rules of algebra I know of.
Can somebody break it down for me with several algebraic intermediate steps so I can see how you can simplify ( x/(x + 1) ) – ( x/(x + 2) ) to x/( (x + 1)(x + 2) ) ?
Originally posted by humyOr more simply just multiply each side of the equation by (x+1)(x+2):
Arr, after not getting it for ages, I suddenly got it just literally only one min after I posted this!
Sorry about that.
Perhaps this would be a nice bit of maths exercise for one of you if you don't look at my answer below first.
The answer is:
( x/(x + 1) ) – ( x/(x + 2) )
= ( x(x + 2) /((x + 1) (x + 2) ) ) – ( x(x + 1)/((x + 1) (x + 2 ...[text shortened]...
= x( x + 1 – x + 2 ) / ((x + 1)(x + 2))
= x( 1 ) / ((x + 1)(x + 2))
= x / ((x + 1)(x + 2))
Originally posted by humyThere doesn't seem to be a simple answer to the sum. Try the following Wolfram Alpha query:
What I really want to know, far more than the equation for the above pattern (although that would be far better than nothing! ), is the general algebraic formula for:
∑ [X = x, X = +∞] 1/( (X^2)(X + 1) ) where (x>0, x ∈ ℕ)
This is so, to work out that sum (which is for a very important probability model that indirectly helps to solve the problem of in ...[text shortened]... r too high. And the approximation gets better and better with every increase in x.