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Determine The Limit Of The Sequence Or State That The Sequence Diverges. An=2−N22

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The sequence is given by An = 2 - n/2.

To determine whether this sequence diverges or converges, we need to examine the limit as n approaches infinity.

The limit of a sequence An as n approaches infinity is represented as lim n->∞ An.

Substitute the expression of An into this formula gives us:

lim n->∞ (2 - n/2).

As n gets larger and larger (approaches infinity), the term -n/2 will also get increasingly larger (more negative). This means that the value of the expression will go to negative infinity.

In other words, as n increases towards infinity, (2 - n/2) decreases without bound. Thus, the limit does not exist, meaning the sequence diverges towards negative infinity.

Therefore, we can conclude that the sequence An diverges to negative infinity.

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