Triangle Numbers

20 people at a party gives gifts to each other. How many gifts were given?[br]20 people at a party shake each others hands. How many handshakes were there?[br]An ice cream store has 20 flavors. How many [i]different [/i]ways can you pick 2 different flavors?[br]When Gauss was very young he found a fast way to add up all the numbers from 1 to 100. Can you?[br]What is the nth triangle number?
Triangle Numbers

Information: Triangle Numbers