handshake problem

There are 20 people in a room. Every person must shake hands with every person in the room. How many hand shakes have taken place?

use algorithim

(n-1)+(n-2)+(n-3)...

20-1=19 people

19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 190 handshakes