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.