Integrating sums of functions
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A sum and an integral both represent ways of adding things up, but they operate in different settings. A sum deals with discrete quantities — it adds up separate, countable items such as numbers in a list or terms in a sequence. When you sum something, you are essentially moving in steps, taking one term after another and combining them. For example, if you wanted to know the total of the first ten natural numbers, you would compute 1 2 3 … 10. Each term is distinct, and there’s a clear “next” o
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