Question

Let the partial sum of a series be sn = ∑ k=l to n ak. The series converges to s if the __________________ converges to s.

A. Sequence of partial sums.
B. Sum of ak as k approaches infinity.
C. Sum of ak as n approaches infinity.
D. Sum of s as n approaches infinity.

Answer 1

The series converges to s when the sequence of partial sums converges to s. The correct answer is A. Sequence of partial sums.

Step-by-step explanation:

The series converges to s if the sequence of partial sums converges to s. Therefore, the correct answer to the given question is A. Sequence of partial sums. In the context of series and summation, convergence of a series is defined as the limit of the sequence of its partial sums. If the sequence of partial sums approaches a finite limit as n approaches infinity, then the series is said to be convergent.