2) The sequence can approach one of the two infinities. Either positive or negative infinity. Example : 1, 2, 4, 8, 16, . . . approaches positive infinity, while the sequence : -1, -2, -4, -8, -16, . . . approaches negative infinity.
3) The sequence has no limit. The big deal here is that the limit has to approach a single value or go towards one of the infinities. (Note: infinity is not a number. It means that the sequence increases without bound!) Example: 1, -2, 3, 4, 5, -6, . . . doesn't approach one single value. The purple odd numbers 1, 3, 5, 7, . . . go toward positive infinity, while the pink even numbers -2, -4, -6, . . . go toward negative infinity. Result: since they don't approach the same thing, there is no limit.
Therefore, the limit is 1.
Therefore, the limit is positive infinity.
Therefore, there is no limit. (Remember the 3 possibilities at the beginning?)
Therefore, the limit is 0 because they both approach the same number.