apery.mws 1. limit(b[n]/a[n],n = infinity) = zeta(3); 2. a[n]; is a positive integer and d[n]^3*b[n]; is an integer, where d[n]; is the lcm of 1,..., n; 3. Both a[n]; and b[n]; satisfy a simple linear recurrence Recurrence satisfied by a[n]; Recurrence satisfied by b[n]; Indefinite sum inside b[n]; These operators do not generate a D-finite ideal Now, this is D-finite Building up the summand Creative telescoping b[n]; satisfies the same recurrence as a[n]; The right-hand side telescopes to 0 4. Asymptotic behaviour of c[n];:= a[n]*zeta(3)-b[n]; 5. 0 < zeta(3)-b[n]/a[n]; 6. Conclusion