Triangle Numbers
Algebra
Level
3
To construct the \(n\)th triangle number, start with a row of \(n\) dots. Then add a row with \(n-1\) dots. Continue, adding a row with one fewer dot in every step, until a row with one dot is added. The drawing above show the second through sixth triangle numbers: \(T_2 = 3, T_3 = 6, T_4 = 10, T_5 = 15, T_6 = 21\).
How much is \(T_{99} + T_{100}\)?
Try to answer without a calculator.
Hint: Algebraic answers are great; geometric answers may be even greater!
by
Arjen Vreugdenhil