Let
Tr = 1
2
 r(r+1)
denote the rth triangular number. Prove that the sum of the reciprocals of the first n triangular numbers is approximately equal to 2 when n is large, that is:
n
å
r=1 
 1
Tr
 = 1
T1
 + 1
T2
 + 1
T3
 + ... + 1
Tn
 @ 2

Hence show that the sum of the reciprocals of the first n triangular numbers tends to 2 as n tends to infinity.