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Apr3-12, 01:34 AM
P: 280
[tex]\lim_{n\rightarrow \infty} \left (\left ( 1+\frac{1}{n} \right )^n \right)^2[/tex]
[tex]\left ( \lim_{n\rightarrow \infty} \left ( 1+\frac{1}{n} \right )^n \right)^2[/tex]

So let's just ignore the squaring for now. Whatever we find, we will square it.

[tex] I =\lim_{n\rightarrow \infty} \left ( 1+\frac{1}{n} \right )^n[/tex]

[tex] ln(I) =\lim_{n\rightarrow \infty} ln\left (\left ( 1+\frac{1}{n} \right )^n \right )[/tex]
[tex] ln(I) =\lim_{n\rightarrow \infty} nln\left (1+\frac{1}{n} \right )[/tex]

This is an indeterminate form of zero times infinity. Let
[tex] N = \frac{1}{n}[/tex]
[tex] ln(I) =\lim_{n\rightarrow 0} \frac{ln\left (1+N \right )}{N}[/tex]

Can you take it from here?