Answer:
B) False
Step-by-step explanation:
A series that tends toward a single number is called a convergent series, not a divergent series.
The statement is false; a series that tends towards a single number is known as a convergent series, not a divergent series. A convergent series is one where the sum of its terms approaches a finite value, whereas a divergent series does not approach any limit. So, the correct answer is option B) False.
The question you've asked relates to series in mathematics. The statement in the question is false because a series that tends toward a single number is called a convergent series, not a divergent one. A convergent series is one in which the sum of its terms approaches a specific value as more terms are added. In contrast, a divergent series is one that does not tend toward any limit when more terms are added.
For example, the geometric series with a common ratio |r| < 1 is a classic example of a convergent series because its terms become smaller and approach zero, allowing for the sum to converge to a finite number. If, however, the common ratio is |r| ≥ 1, the terms do not get smaller and the series does not converge to a single number; this is what we call a divergent series.
Therefore, when considering whether an infinite series converges or diverges, we often use various tests such as the ratio test, which is based on the behavior of the series terms.
In conclusion, the correct option to the question posed is B) False because a series that tends toward a single number is known as a convergent series.
