Recurrence relations, convergence tests, identifying sequences
18
votes
2answers
150 views
+500
Conjectural closed-form representations of sums, products or integrals
What are some examples of infinite sums, products or definite integrals that have conjectural closed form representations that were confirmed by numerical calculations up to whatever maximum precision ...
11
votes
2answers
192 views
+50
All nested partial sums of a sequence tend to $0$. Is the sequence constant?
$S^0:\mathbb N\to \Bbb R$ is a function. For any $m\in \Bbb N$, we define
$$S^m:\Bbb N\to \Bbb R$$
$$S^m(n)=\sum_{k=1}^n S^{m-1}(k)$$
For each $m\in \Bbb N$, we have:
$$\lim_{n \to \infty}S^m(n)=0$$
...
