The value of x that satisfies the relation
$x = 1 - x + x^{2} - x^{3} + x^{4} - x^{5} + . . . . . . . . \infty$

2 c o s 3 6^{\circ}

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2 c o s 144^{\circ}

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2 s i n 18^{\circ}

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none

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Solution

The correct option is A $2 c o s 3 6^{\circ}$
The series $1 - x + x^{2} - . . . .$ form $G P$ with $a = 1, r = - x$
Sum of infinte GP is $x = \frac{a}{1 - r} x = \frac{1}{1 + x} x + x^{2} = 1 x^{2} + x - 1 = 0$
By quadratic formulae
$x = \frac{- 1 \pm \sqrt{1 + 4}}{2} 2 \frac{- 1 \pm \sqrt{5}}{4} 2 cos 36^{\circ}$

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Similar questions

Q. The value of

x

that satisfies the relation

x = 1 - x + x^{2} - x^{3} + x^{4} - x^{5} + . \infty

| x | < 1

Q. If

x

is a rational number satisfying

(1 - x) (1 + x + x^{2} + x^{3} + x^{4})

= \frac{31}{32} .

Then

1 + x + x^{2} + x^{3} + x^{4} + x^{5}

If $(1 - x) (1 + x + x^{2} + x^{3} + x^{4})$ is $\frac{31}{32}$ and $x$ is a rational number. Find the value of $1 + x + x^{2} + x^{3} + x^{4} + x^{5}$ .

Q. Find the value of

x^{5} - x^{4} + x^{3} - x^{2} + 1

when

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x is a rational number satisfying (1-x) (1+x+x²+x³+x⁴) = .

Then 1+x+x²+x³+x⁴+X⁵ is

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The value of x that satisfies the relation x=1−x+x2−x3+x4−x5+........∞

The correct option is A 2cos36∘The series 1−x+x2−.... form GP with a=1,r=−xSum of infinte GP is x=a1−rx=11+xx+x2=1x2+x−1=0By quadratic formulae x=−1±√1+422−1±√542cos36∘

The value of x that satisfies the relation
$x = 1 - x + x^{2} - x^{3} + x^{4} - x^{5} + . . . . . . . . \infty$