Show HN: Asymptotic Growth Order Calculator (franklin.dyer.me)

I'm an undergraduate student and for my math honors thesis I'm studying asymptotic growth orders, the kind you usually see written in "big-Theta" notation to describe an algorithm's time/memory usage. The most interesting part was studying how to compute the growth order of the sequence of partial sums of a given sequence - that is, the growth order of (a_1 + ... + a_n), in terms of the growth order of (a_n).

So I thought I would make a little web calculator for playing around with this. Enjoy! :-)

Some things to try:

1. The sums of the harmonic sequence (1/n) diverge, but can you find a faster-decaying sequence that also has diverging sums?

2. Can you make the growth order log(log(log(n))) using only one register?

3. What happens when you apply Σ⅟ΣΣΣ (applied from right to left) to any growth order, and why?