I don't know... here's a prompt query for a standard problem in introductory integral calculus, and it seems to go pretty smoothly from a discrete arithmetical series into the continuous integral:
"Consider the following word problem: "A 100 meter long chain is hanging off the end of a cliff. It weighs one metric ton. How much physical work is required to pull the chain to the top of the cliff if we discretize the problem such that one meter is pulled up at a time?" Note that the remaining chain gets lighter after each lifting step. Find the equation that describes this discrete problem and from that, generate the continuous expression and provide the Latex code for it."
"Consider the following word problem: "A 100 meter long chain is hanging off the end of a cliff. It weighs one metric ton. How much physical work is required to pull the chain to the top of the cliff if we discretize the problem such that one meter is pulled up at a time?" Note that the remaining chain gets lighter after each lifting step. Find the equation that describes this discrete problem and from that, generate the continuous expression and provide the Latex code for it."