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Reciprocal Triangles
Age 16 to 18
Challenge Level 
The algebraic expression for $r$th triangular number is
$$T_r = \frac{1}{2} r(r+1) $$
The expression that you are trying to evaluate is $$\sum_{r=1}^{n} \frac{1}{T_r} = \frac{1}{T_1} + \frac{1}{T_2} + \frac{1}{T_3} + ... + \frac{1}{T_n} \cong 2 $$
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