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I know that [tex]\sum[/tex] is used for an infinite sum, and [tex]\prod[/tex] is used for an infinite product. But are there any more of that type?
An infinite sum/product is a series of numbers that continues forever. In other words, there is no specific end point to the series.
An infinite sum adds each term in the series together, while an infinite product multiplies each term in the series together. In other words, an infinite sum is the addition of terms and an infinite product is the multiplication of terms.
Infinite sums/products are used to represent the total value of a series that continues forever. They are also used in many mathematical equations and proofs, as well as in real-world applications such as finance, physics, and engineering.
Yes, an infinite sum/product can have a finite value if the terms in the series approach 0 as the series continues. This is known as a convergent series/product. However, if the terms in the series do not approach 0, then the infinite sum/product will not have a finite value and is known as a divergent series/product.
Infinite sums/products are used in various fields such as finance, physics, and engineering to model and solve problems involving continuous growth or decay. For example, they can be used to calculate compound interest, determine the total distance traveled by an object in motion, or find the total resistance in an electrical circuit.