- #1
opticaltempest
- 135
- 0
How do I evaluate this limit?
[tex]
\mathop {\lim }\limits_{n \to \infty } \left( {\frac{2}{3}} \right)^n
[/tex]
Is this the correct approach?
[tex]
{\rm{Let}} \; \; \; y = \mathop {\lim }\limits_{n \to \infty } \left( {\frac{2}{3}} \right)^n
[/tex]
[tex]
\ln y = \mathop {\lim }\limits_{n \to \infty } \ln \left[ {\left( {\frac{2}{3}} \right)^n } \right]
[/tex]
[tex]
\ln y = \mathop {\lim }\limits_{n \to \infty } \left[ {n \cdot \ln \left( {\frac{2}{3}} \right)} \right]
[/tex]
I am stuck at this step. I don't see a way to manipulate the limit into a
form that L'Hopital's Rule will apply. I know the limit evaluates to 0.
[tex]
\mathop {\lim }\limits_{n \to \infty } \left( {\frac{2}{3}} \right)^n
[/tex]
Is this the correct approach?
[tex]
{\rm{Let}} \; \; \; y = \mathop {\lim }\limits_{n \to \infty } \left( {\frac{2}{3}} \right)^n
[/tex]
[tex]
\ln y = \mathop {\lim }\limits_{n \to \infty } \ln \left[ {\left( {\frac{2}{3}} \right)^n } \right]
[/tex]
[tex]
\ln y = \mathop {\lim }\limits_{n \to \infty } \left[ {n \cdot \ln \left( {\frac{2}{3}} \right)} \right]
[/tex]
I am stuck at this step. I don't see a way to manipulate the limit into a
form that L'Hopital's Rule will apply. I know the limit evaluates to 0.
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