I did first and second year maths at university, but I've possibly forgotten more than a remember, it seems since I no proofs sprang to mind other than those you've mentioned.

I'm now thinking I'll have to dig into my old maths books. I do recall spending a large amount of time messing around with Taylor series, so presumably I must've been doing it for a reason, but can't for the life of me remember what!

I often wish I'd stuck with it, rather than switching to Economics. There's definitely something pleasing about the rigor required in mathematics.