Question

Assume that the series ∑ ak converges, then lim an as n goes to infinity equals:

A. 0.
B. [infinity].
C. A finite real number.
D. The limit does not exist.

Answer 1

The limit of an as n goes to infinity, given that the series ∑ ak converges, is a finite real number.

Step-by-step explanation:

The correct answer is option C. A finite real number.

If the series ∑ ak converges, it means that the terms ak eventually become very small as n goes to infinity. Therefore, as n approaches infinity, the terms an also approach zero. This is because a convergent series has a limit of zero.

For example, consider the series 1/n. As n approaches infinity, the terms 1/n approach zero. So the limit of an as n goes to infinity is indeed 0 (option A).

Therefore, the correct answer is C. A finite real number.