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# What does it mean to say that lim_{n → ∞} a_{n} = 8?

The terms a_{n} approach infinity as 8 approaches n.

The terms a_{n} approach 8 as n becomes small.

The terms a_{n} approach 8 as n becomes large.

The terms a_{n} approach infinity as n become large.

The terms a_{n} approach -infinity as 8 approaches n.

**Solution:**

Limits in maths are unique real numbers.

Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as lim_{x→c} f(x) = L.

It is read as “the limit of f of x, as x approaches c equals L”.

\(\lim_{n \to 0} a_{n} = 8\) means the terms a_{n} approach 8 as n becomes large.

Option (iii) is the answer.

**Example:**

\(\lim_{x \to 0} = \frac{1}{x} = \infty\) means the term 1/x approach to ∞, a large value, as n becomes smaller and smaller.

We may also note that the limit of function is said to exist if \(\lim_{x \to a} f(x) = l\) where l is a finite value.

However, in the above example it can also be stated that the limit of function does not exist.

## What does it mean to say that lim_{n → ∞} a_{n} = 8?

**Summary:**

Lim_{n → ∞} a_{n} = 8 means the terms a_{n} approach 8 as n becomes large.

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