The Mad Sum

There are 9 zeroes on 1000000000. $A=1+2+3+\ldots+999999999+1000000000$ $2A=1000000001+1000000001+\ldots+1000000001$ $2A=1000000001\times1000000000$ $A= \frac{1000000001\times1000000000}{2}=1000000001\times500000000$ $A=\boxed{500000000500000000}$

$1 + 2 + 3 + \cdots + 999999998 + 999999999 + 1000000000 = \frac { 1000000001 \times 1000000000 } { 2 } = 1000000001 \times 500000000 = 500000000500000000 \text { , so the answer is \boxed { \text { 500000000500000000 } } }. \text { It is also read as five hundred quintillion five hundred million. }$ .

A simple equation: 1 + 2 + 3 + 4 +...+ n-1 + n = (n+1) * n/2. I have absolutely no idea for what numbers that holds and for what it doesn't, I only came up with this while solving this problem (I might have seen it somewhere but I really can't recall). I tried this with simple numbers (like n=8, n=20, n=22) and noticed a pattern so I applied it to this huge one. Still, I thought it would be nice to share this simple trick.