Which statement correctly describes convergent infinite series in the discussed context?

Which statement correctly describes convergent infinite series in the discussed context?

• A. Infinitely many steps always diverge to infinity.
• B. Infinitely many steps can still add up to a finite total distance or time (e.g., 1/2 + 1/4 + 1/8 ...).
• C. A finite number of steps cannot reach a finite limit.
• D. The sum of infinite terms cannot be finite.

Answer: (B)

Convergent infinite series are about the total amount you accumulate approaching a single finite value, even though you keep adding infinitely many terms. The running total of partial sums gets closer and closer to a specific number. The example 1/2 + 1/4 + 1/8 + … shows this clearly: each term is smaller than the last, and the sum approaches 1. So, infinitely many steps can still add up to a finite total distance or time. The other ideas don’t fit this behavior. Some series can grow without bound, but convergence is about reaching a finite limit. Also, finite sums of a finite number of terms are finite, so saying that a finite number of steps cannot reach a finite limit isn’t true in general. And it’s possible for an infinite series to have a finite sum, which makes the statement that the sum of infinite terms cannot be finite incorrect.

Convergent infinite series are about the total amount you accumulate approaching a single finite value, even though you keep adding infinitely many terms. The running total of partial sums gets closer and closer to a specific number. The example 1/2 + 1/4 + 1/8 + … shows this clearly: each term is smaller than the last, and the sum approaches 1. So, infinitely many steps can still add up to a finite total distance or time.

The other ideas don’t fit this behavior. Some series can grow without bound, but convergence is about reaching a finite limit. Also, finite sums of a finite number of terms are finite, so saying that a finite number of steps cannot reach a finite limit isn’t true in general. And it’s possible for an infinite series to have a finite sum, which makes the statement that the sum of infinite terms cannot be finite incorrect.