Find the value of the limit $\lim _ { k \rightarrow \infty } \left( 1 + \frac { 1 } { 10 ^ { k } } \right) ^ { 10 ^ { 1 } }$ .
A)0
B)1
C)2
D) $e$
E)3
F) $\pi$
G)4
H) $\infty$

Question

Find the value of the limit $\lim _ { k \rightarrow \infty } \left( 1 + \frac { 1 } { 10 ^ { k } } \right) ^ { 10 ^ { 1 } }$ .
A)0
B)1
C)2
D) $e$ 
E)3
F) $\pi$ 
G)4
H) $\infty$

Quizplus · Accepted Answer

This limit is a classic example of the definition of the natural number $e$. The expression can be rewritten in the form of $\left(1 + \frac{1}{n}\right)^n$ as $k \rightarrow \infty$, which approaches $e$ as $n$ approaches infinity.

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Find the Value of the Limit $\lim _ { k \rightarrow \infty } \left( 1 + \frac { 1 } { 10 ^ { k } } \right) ^ { 10 ^ { 1 } }$