sequences

The sequences (an), (bn), and (cn) are defined by a0 = 1, b0 = 0, c0 = 0, and
an = an-1 + cn-1 / n, bn = bn-1 + an-1 / n, cn = cn-1 + bn-1 / n
for all n>=1.

Prove that:
| an – (n+1)/3 | =1