Skip over navigation
Reciprocal Triangles
Age 16 to 18
Challenge Level 
The algebraic expression for rth 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
You may also like
Telescoping Series
Find S_r = 1^r + 2^r + 3^r + ... + n^r where r is any fixed positive integer in terms of S_1, S_2, ... S_{r-1}.
OK! Now Prove It
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?