Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

Reciprocal Triangles

Stage: 5 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 $$\sum_{r=1}^{n} \frac{1}{T_r} = \frac{1}{T_1} + \frac{1}{T_2} + \frac{1}{T_3} + ... + \frac{1}{T_n} \cong 2 $$