The sequence you’ve presented is an example of a geometric series where each term is obtained by multiplying the previous term by . The first term is and the common ratio is . This series represents the sum of an infinite geometric progression, which converges to where is the first term and . In this case, the sum converges to .

This type of series not only appears in mathematics, but also shows up in various real-world contexts like finance and population modeling, where quantities can decrease progressively. For example, when dealing with investments that yield returns that become smaller over time, understanding how to sum these infinitesimal returns can provide insights into long-term profitability or depreciation.