Which term describes a series formed by rapidly growing terms?

Which term describes a series formed by rapidly growing terms?

• A. Divergent series
• B. Convergent series
• C. Arithmetic series
• D. Bounded series

Answer: (A)

A series is described as divergent when the sum of its terms does not approach a finite limit as more terms are added. In the context of a series with rapidly growing terms, the partial sums tend to increase without bound, leading to an infinite sum that does not settle at any specific value. For example, consider a simple series like the sum of the natural numbers: 1 + 2 + 3 + ... This series grows larger without limit, demonstrating divergence. In contrast, convergent series approach a specific value as more terms are included. An arithmetic series involves a constant difference between consecutive terms, and a bounded series means that the terms do not exceed certain limits. Therefore, when a series has terms that grow rapidly, it is categorized as a divergent series.

A series is described as divergent when the sum of its terms does not approach a finite limit as more terms are added. In the context of a series with rapidly growing terms, the partial sums tend to increase without bound, leading to an infinite sum that does not settle at any specific value.

For example, consider a simple series like the sum of the natural numbers: 1 + 2 + 3 + ... This series grows larger without limit, demonstrating divergence. In contrast, convergent series approach a specific value as more terms are included. An arithmetic series involves a constant difference between consecutive terms, and a bounded series means that the terms do not exceed certain limits. Therefore, when a series has terms that grow rapidly, it is categorized as a divergent series.