Hey /sci/
Im not a typical browser, and a first time poster right now, but I've been scratching my head on this problem for a better part of a couple days now and want to see if anyone can assist me with the last piece.
Basically, so lets say function s(n) = 1+2+3+...+n
Its easy to work out that that can be worked out to s(n) = (n+1)(n/2)
Lets call a new function q(n) = s(1)+s(2)+s(3)+...+s(n)
Is there a way of simplifying that algebraically? Can I write that into a function of coeficients that wont need me to loop over values?
As I said, this is the last piece of the puzzle I have been working on, and if it can be simplified further that would be great. I thought I made some work into this, thought it might have been related to Pascals triangle somehw but it turns out I was looking at it wrong. I found that:
q(1) = 1
q(2) = +1+2
q(3) = +1+2+3
q(4) = +1+2+3+4
...
q(n) = +1+2+3+4+...+n
so that:
q(n) = (n)(1)+(n-1)(2)+(n-2)(3)+...+(n-1)(2)+(n)(1)
Maybe something can be made out of this.
Im not a typical browser, and a first time poster right now, but I've been scratching my head on this problem for a better part of a couple days now and want to see if anyone can assist me with the last piece.
Basically, so lets say function s(n) = 1+2+3+...+n
Its easy to work out that that can be worked out to s(n) = (n+1)(n/2)
Lets call a new function q(n) = s(1)+s(2)+s(3)+...+s(n)
Is there a way of simplifying that algebraically? Can I write that into a function of coeficients that wont need me to loop over values?
As I said, this is the last piece of the puzzle I have been working on, and if it can be simplified further that would be great. I thought I made some work into this, thought it might have been related to Pascals triangle somehw but it turns out I was looking at it wrong. I found that:
q(1) = 1
q(2) = +1+2
q(3) = +1+2+3
q(4) = +1+2+3+4
...
q(n) = +1+2+3+4+...+n
so that:
q(n) = (n)(1)+(n-1)(2)+(n-2)(3)+...+(n-1)(2)+(n)(1)
Maybe something can be made out of this.
