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limit of infinity

i'm wondering is this valid?

\(\lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad { (1\frac { 1 }{ x } ) }^{ x }\quad =\quad ({ \frac { 1(x)+1 }{ x } ) }^{ x }\quad =\quad ({ \frac { x+1 }{ x } ) }^{ x }\quad }\) and since \(\infty +1\) does not make much of a difference so is still \(\infty\) then \({ (\frac { x }{ x } ) }^{ x }\quad =\quad 1\quad\) if we treat \(\infty\) like a number.

therfore \(\quad \lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad 1\quad }\)

Note by Shufay Ung
2 years, 6 months ago

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You can't treat infinity like a number that's where the fallacy begins. Ronak Agarwal · 2 years, 6 months ago

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