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