Question

Find x if x+ x^2 + x^3 + x^4 ... infinity = 2/3 for [ -1 < x < 1]​

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$


$\boxed{ \underline{ \sf{GIVEN : }}}$


$x \: + \: {x}^{2} \: + \: {x}^{3} + \: {x}^{4} \: ... \: \infty \: = \: \frac{2}{3}$

where (-1 < x < 1)


$\boxed{ \underline{ \sf{TO \: FIND : \: x }}}$


$\boxed{ \underline{ \sf{SOLUTION : }}}$


As the sequence is in G.P ,so the formula for ${S}_{\infty} \: = \: \frac{a}{1 - r}$.

a = x , r = $\frac{ {x}^{2} }{x}$ = x


A/Q,

$\implies \: S_{ \infty} \: = \: \frac{2}{3}$

$\implies \: \frac{a}{1 - r} \: = \: \frac{2}{3}$

$\implies \: \frac{x}{1 - x} = \frac{2}{3}$

$\implies \: 2(1 - x) \: = \: 3x$

$\implies \: 2 - 2x \: = \: 3x$

$\implies \: 5x = 2$

$\implies \: x \: = \: \frac{2}{5}$


$\boxed{ \sf{ \bf{ \therefore \: x = \frac{2}{5} }}}$

Answer 2

$\mathcal{\red{\huge{Heya\:mate\:!!}}}$

$\mathtt{Here\:is\:ur\:@nswer}$⎇

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$\textsf{\pink{Q.}}$Find x if x+ x^2 + x^3 + x^4 ... infinity = 2/3 for [ -1 < x < 1]​

$\textsf{\pink{Ans.}}$
$\bold{ Step-by-step\: explanation\::-}$

{1 - r}= 2/3

{x}{1 - x} = 2/3

2(1 - x) =3x

2 - 2x =  3x

OR  5x = 2

 OR x = 2/5

THUS X = 2/5

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