Final answer:
The correct answer is C. (sn + tn) converges to s. If (sn) converges to a positive real number s and (tn) is any sequence, adding the terms of (sn) and (tn) will result in a sequence that converges to the sum of s and the limit of (tn).
Step-by-step explanation:
The correct answer is C. (sn + tn) converges to s.
If (sn) converges to a positive real number s, it means that the terms of the sequence (sn) get arbitrarily close to s as n approaches infinity. Similarly, if (tn) is any sequence, the terms of tn can also approach a certain value as n approaches infinity. Therefore, when we add the terms of (sn) and (tn), the resulting sequence (sn + tn) will also converge to the sum of s and the limit of (tn).
For example, if (sn) = 1/n and (tn) = 2, then (sn) converges to 0 and (tn) converges to 2. When we add the terms of (sn) and (tn), we get (sn + tn) = (1/n + 2), which converges to 2 as n approaches infinity.