I don't think it's unreasonable to expect it. E.g. clang -O1 (https://godbolt.org/g/7qzSF9 ) is able to use the closed form for a sum on a simple C++ loop. It's not unreasonable that a language with deeper introspection could identify more closed forms. I agree that I don't think the Haskell maintainers would put this specific example in, but I wonder whether they could build it up from simpler primitives.

Haskell optimizer does not feature an arithmetic Oracle nor polynomial optimizer. It cannot even optimize Peano arithmetic much less a series.

This might be fixed some time or never. There is little push for ultimate performance and actually identifying arithmetic forms in recursive loops in the front-end is hard. (Heck it sometimes fails to tail optimize.)

I'd be interested to see how this weighs out in 5-10 years. Since there's no I/O here, I don't see why a clever compiler writer couldn't optimize this whole expression away at compile time, generating an executable just prints a constant.