For the special case when&nbsp;\(n = 1\) and \(R = 100\), it is interesting to examine what happens to \(A\) as&nbsp;\(k\) tends to infinity.
That is, what is the limiting value of \[
A = P \left( 1+\frac{1}{k} \right)^{k}
\] as&nbsp;\(k \to \infty\)?
It turns out that \[
\lim_{k \to \infty} \left( 1 + \frac{1}{k} \right)^k
\] exists as it is monotonically increasing and bounded above. We denote the above limit by the constant \(e\), and \[
e \approx 2.7178281828\ldots
\] This constant is called the Euler's constant.
Hence \[
\lim_{k \to \infty} A = Pe.
\]
We shall see later in a later module Differentiation the role the Euler constant \(e\) plays.

For the special case when \(n = 1\) and \(R = 100\), it is interesting to examine what happens to \(A\) as \(k\) tends to infinity.

That is, what is the limiting value of 
\[
A = P \left( 1+\frac{1}{k} \right)^{k}
\]
as \(k \to \infty\)?

It turns out that 
\[
\lim_{k \to \infty} \left( 1 + \frac{1}{k} \right)^k
\]
exists as it is monotonically increasing and bounded above.  We denote the above limit by the constant \(e\), and 
\[
e \approx 2.7178281828\ldots
\] 
This constant is called the *Euler's constant*.

We shall see later in a later module **Differentiation** the role the Euler constant \(e\) plays.

Pre-cursor to natural base \(e\)

Pre-cursor to natural base \(e\)