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

\frac{- 1 \pm \sqrt{5}}{2}

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\frac{- 1 \pm 3 i}{2}

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Solution

The correct option is C $\frac{- 1 \pm \sqrt{5}}{2}$
Here the first term is $a$
Common ratio is given by $- x$
The sum of infinite series is of an GP is given by $a1−rx=dfrac11+xx2+x=1x2+x−1=0$
Using quadratic formulae $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Here $a = 1 b = 1 c = - 1$
$⟹ x = \frac{- 1 \pm \sqrt{1 + 4}}{2} x = \frac{- 1 \pm \sqrt{5}}{2}$

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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

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}

\int (x + x^{2} + x^{3} + x^{4})

dx is equal to

Q. Find the value of

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

when

x = 2

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

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

The correct option is C −1±√52Here the first term is a Common ratio is given by −xThe sum of infinite series is of an GP is given by a1−rx=dfrac11+xx2+x=1x2+x−1=0Using quadratic formulae −b±√b2−4ac2aHere a=1b=1c=−1⟹x=−1±√1+42x=−1±√52

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