Well, I know what factorials are, it is n*(n-1)*(n-2), etc. until you've gone all the way down to zero. What i'm looking for is a way to express n+(n-1)+(n-2), etc. Do you know of any way to write this?
3n-3, I expect. I may be wrong.
Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.
(I think) this topic's been done before, but anyway...
You are asking how to express Triangular Numbers.
You can do this by using this formula: n(n+1)
or also 0.5n² + 0.5n.
Yep, just recently covered here.
The question was adding up the numbers 1,2,3,4,5 (your problem is just like 5,4,3,2,1) but my answer included being able to add things like 5,6,7,8,9 (ie the general solution) ... and Milos rounded out the whole discussion.