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

#Calculus

Easy Math Editor

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Comments

You can't treat infinity like a number that's where the fallacy begins.

Ronak Agarwal - 6 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$