Final answer:
The largest possible limit for a subsequence of (sn&tn) depends on the limits of sn and tn. If either sn or tn has a limit of infinity, the largest possible limit of the subsequence is infinity. If both sn and tn have finite limits, the largest possible limit is the product of their limits. If either sn or tn does not have a limit, the largest possible limit is undefined.
Step-by-step explanation:
The largest possible limit for a subsequence of (sn&tn) can be found by considering the limits of both sn and tn.
If the limit of sn is infinity and the limit of tn is a finite number, then the largest possible limit of the subsequence is infinity.
If the limit of tn is zero and the limit of sn is a finite number, then the largest possible limit is zero.
If both sn and tn have finite limits, then the largest possible limit is the product of the limits of sn and tn.
In the case where either sn or tn does not have a limit, then the largest possible limit is undefined.