Final answer:
If the sequences (sn) and (tn) satisfy the conditions where 0 < sn < tn, sn approaches s, and tn approaches t, then the product of sn and tn also converges.
Step-by-step explanation:
If the sequences (sn) and (tn) satisfy the conditions where 0 < sn < tn, sn approaches s, and tn approaches t, then the product of sn and tn also converges. To understand why, we can use the fact that if a sequence converges, then the product of that sequence with any other convergent sequence also converges.
Since sn → s and tn → t, we know that the sequence (sn) converges to s and the sequence (tn) converges to t. By the property of limits, we have the limit of the product of sn and tn as the product of the limits of sn and tn, which is s * t.
Therefore, the product sequence sn * tn converges to the product of s and t.