1 Is Equal to 0,99999...

$x\quad =\quad 0.999999...\\ 10x\quad =\quad 9.99999...\\ 10x\quad -\quad x\quad =\quad 9.000....\\ x=1$

$0.9999...\quad =\quad \frac { 9 }{ 10 } *{ \frac { 1 }{ 10 } }^{ 0 }+\frac { 9 }{ 10 } *{ \frac { 1 }{ 10 } }^{ 1 }+....\frac { 9 }{ 10 } *{ \frac { 1 }{ 10 } }^{ n }\\ \\ Using\quad infinite\quad sum\quad formula\quad for\quad a\quad geometric\quad series:\\ \\ \frac { \frac { 9 }{ 10 } }{ 1-\frac { 1 }{ 10 } } \quad =\quad \frac { \frac { 9 }{ 10 } }{ \frac { 9 }{ 10 } } \quad =\quad 1$

#Algebra #Numbers #Series #InfiniteSum #GeometricSequence

Easy Math Editor

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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}`	$\frac{2}{3}$
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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}`	$\boxed{123}$