Question

Which statement is true about the series with a common ratio (r)?

Options:

a.The series converges because r<1.
b.The series diverges because ∣r∣<1.
c.The series diverges because ∣r∣>1.
d. The series converges because r>1.

Answer 1

The statement that is true about a series with a common ratio (r) is option a: The series converges because r<1.

Step-by-step explanation:

The statement that is true about a series with a common ratio (r) is option a: The series converges because r<1.

In a geometric series, if the common ratio (r) is between -1 and 1, the series converges. This means that as you continue adding terms to the series, the sum gets closer and closer to a finite value. If the common ratio is less than 1 (r<1), the series converges.

For example, if you have a geometric series with a common ratio of 1/2, each term in the series is half the value of the previous term. As you add more terms, the sum approaches 1.