[Inori]

If you're not going to stick to the conventional rules that come along with limits and summinations, then don't use them? Just write out the series as you did below and don't even try to use proper notation if "it's just psudocode", what's even the point if you're writing out an expression. The sigma notation is the limit of summation in itself, you don't need to write it out twice. If you want to do the limit of a series then just google it, because you wrote out the limit of an expression. Obviously the second one isn't a product, it's the limit of an expression as x approaches infinity.

tl;dr Don't try to look smart by writing expressions that you don't understand or don't bother to check, just stick to stuff you understand.

I mean, I'm in 10th grade math and trying to learn some stuff on my own time, but by all means rip me to shreds