Final answer:
To determine whether a sequence converges or diverges, we examine the behavior of the terms as we go further in the sequence. If the terms approach a single value, the sequence converges, and the limit is that value. If the terms do not approach a single value, the sequence diverges.
Step-by-step explanation:
To determine whether a sequence converges or diverges, we examine the behavior of the terms as we go further in the sequence. If the terms approach a single value, the sequence converges, and the limit is that value. If the terms do not approach a single value, the sequence diverges.
We can find the limit of a convergent sequence by evaluating the terms as we go further. For example, if we have a sequence defined by an expression like a_n = 1/n, as n gets larger, the terms get smaller and closer to 0, so the limit would be 0.
In some cases, a sequence may not converge or diverge because it oscillates between two or more values. In such cases, the limit does not exist.