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!

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