Sequence and series with specific nth term Let $a(1) = 2$ , $a(n+1) = a(n)^2-a(n) + 1$  for $n\geq 1$, Find $$\sum_{n=1}^{\infty} \frac{1}{a(n)}$$ 

(not an answer)
I calculated with Python:
def f(x): return x**2 -x +1

def list_sum(a):
l = []
term = a
for k in range(20):
    l.append(1.0/term)
    term = min(f(term),50000000000)
    print "term=", term
return sum(l)

print list_sum(2)

and the answer seems to be quite close to $1$.
