Wednesday 27 March 2013

limits - $lim _{ nrightarrow infty }{ { left( -1+frac { 1 }{ n } right) }^{ n } } =? $

We know that $$\lim _{ n\rightarrow \infty }{ { \left( 1-\frac { 1 }{ n } \right) }^{ n } } =\frac { 1 }{ e } .$$ However the result of $$\lim _{ n\rightarrow \infty }{ { \left( -1+\frac { 1 }{ n } \right) }^{ n } } $$ is shown in complex form by Wolframalpha . Why complex numbers?




Yes, $-1+\frac { 1 }{ n } < 0 $, but if we write the values from $n=1,2..,10$ , all values will be real. Any opinion? How do you calculate this limit?

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