Question

The series ∑ n=m to infinity an is said to converge provided the sequence (sn) of partial sums converges to a real number S, in which case we define ∑n=m to infinity an is equal to _____.

A. S.
B. 0.
C. Divergent.
D. The limit of (sn).

Answer 1

The value of the converging infinite series ∑ n=m to infinity a_n is equal to the real number S to which the sequence of partial sums converges, hence the correct answer is A. S.

Step-by-step explanation:

The series ∑ n=m to infinity an is said to converge provided the sequence (sn) of partial sums converges to a real number S. In this case, the value of the infinite sum ∑ n=m to infinity an is defined to be equal to S. Therefore, the correct answer to the question "∑ n=m to infinity an is equal to _____" is A. S.