How to simplify recursive eq?

Question

I know how to programatically calculate this, but im not sure how it can be simplified for documentation. Can someone help?

$R = (X\cdot 1) + (X\cdot 2) + (X\cdot 3) + (X\cdot 4) + (X\cdot 5) + (X\cdot 6) + ...$ etc, repeated up to a value of $Y$.

Thanks in advance!

Answer 1

If it is $R = (X\cdot 1) + (X\cdot 2) + (X\cdot 3) + (X\cdot 4) + (X\cdot 5) + (X\cdot 6) + ...+X\cdot \color{blue}{Y}$, then this formula might help: $\sum_{i=0}^Y Xi=X\sum_{i=0}^Y i=X\frac{Y\cdot (Y+1)}{2}$