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I'm not entirely sure how else to word this, but say I've solved a sum like: $$\sum_{n=2}^{\infty} \operatorname{arctanh}(n^{-3})$$ or an integral such as $$\int_1^\infty x^{-x} \,dx$$

Would things like this ever be worth noting or submitting?

Thomas Andrews
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Ryan Goulden
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    Perhaps - if it were new and interesting or particularly short and clever. Your question is too hypothetical. If you've actually done something along these lines, show it to one of your instructors, or ask here for proof-verification. – Ethan Bolker May 02 '18 at 23:28
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    That's fair. I keep a notebook of integrals and sums I've solved that I can't quite find elsewhere. I just don't know if things like that are relevant. I mean, obviously there are ones with a bit of larger signifgance, like perhaps had someone solved $\zeta(3)$ for example. – Ryan Goulden May 02 '18 at 23:31
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    The Monthly of the Mathematical Association of America publishes short notes that sometimes have things like this. So does Mathematics Magazine (less prestigous). There's the arXiv, where they might be notices. If you've several that are related by some thread you could write them up together. Do show them to someone at your school.(+1 for keeping a notebook.) – Ethan Bolker May 02 '18 at 23:38

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