An infinite sequence is a list of numbers that continues forever, with no end point. It can be written in the form of {a1, a2, a3, ... , an, ...}
A finite sequence has a limited number of terms, while an infinite sequence has an unlimited number of terms.
Infinite sequences and series are used in various branches of mathematics and science, such as calculus, number theory, and physics. They also have practical applications in engineering and computer science.
The convergence or divergence of an infinite series can be determined by applying various convergence tests, such as the ratio test, the root test, or the integral test.
Yes, an infinite series can have a finite sum if it is a convergent series. For example, the infinite series 1 + 1/2 + 1/4 + 1/8 + ... has a finite sum of 2.