capital sigma is a big S and capital pi is a big P! they mean "big Sum" and "big Product" and if your math teacher never explained that then fire them
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Never bothered with the product one at all I think? Sums were obviously part of the pre-calc standards I think but product series aren't useful for that I think.
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you need sums for taylor series so they’re pretty common all over but products really only get used in pure math, and off the top of my head mostly in combinatorics, a few places in complex analysis, and number theory
