Question

Is there a shorthand for 'addition factorials' (ie x+(x-1)+(x-2)+(x-3)....)?

Answer 1

Yes, they're called triangular numbers.
\[1+2+3+4+5+6+7+8+9....+x = {x \cdot (x+1) \over 2}\]

Answer 2

Is that what you meant?

Answer 3

wouldnt that be n(x+x-n)/2 ?

Answer 4

http://en.wikipedia.org/wiki/Triangular_number
Gauss proved it right when he was 10, or so they say.

Answer 5

nstarts at zero so that might be n+1

Answer 6

\[\sum_{n=0}^{N}(x-n)\to\ \frac{(n+1)(x+(x-n))}{2} \]

Answer 7

I assumed that n ends at x.