Final answer:
A sequence with an infinite number of ones that does not converge to one could be an alternating sequence like {1, 0, 1, 0, ...} or a sequence with interspersed large numbers such as {1, 2, 1, 3, 1, 4, ...}.
Step-by-step explanation:
An example of a sequence with an infinite number of ones that does not converge to one is a sequence that alternates between one and another value. For instance, consider the sequence an = {1, 0, 1, 0, 1, 0, ...}. This sequence includes an infinite number of ones, but it does not converge to one because it constantly alternates with zero, which interrupts the establishment of one as the limit.
Another example could be an = {1, 2, 1, 3, 1, 4, 1, 5, ...}, which also contains an infinite number of ones but has subsequences that tend to infinity, thus preventing the sequence from converging to one.