Answer:
[tex]^{ \lim}_{n \to \infty} (1+\frac{1}{n})=1[/tex]
Step-by-step explanation:
We want to evaluate the following limit.
[tex]^{ \lim}_{n \to \infty} (1+\frac{1}{n})[/tex]
We need to recall that, limit of a sum is the sum of the limit.
So we need to find each individual limit and add them up.
[tex]^{ \lim}_{n \to \infty} (1+\frac{1}{n})=^{ \lim}_{n \to \infty} (1) +^{ \lim}_{n \to \infty} \frac{1}{n}[/tex]
Recall that, as [tex]n\rightarrow \infty,\frac{1}{n} \rightarrow 0[/tex] and the limit of a constant, gives the same constant value.
This implies that,
[tex]^{ \lim}_{n \to \infty} (1+\frac{1}{n})= 1 +0[/tex]
This gives us,
[tex]^{ \lim}_{n \to \infty} (1+\frac{1}{n})= 1[/tex]
The correct answer is D
