If x < 1 and y=x-x22+x33+x44+……∞ then x=

y=x-x22+x33-....y=log (1+x)ey=1+2x=ey-1 =y+y22+y33+....∞

If x < 1 and y=x-x22+x33+x44+……∞ then x=

y=x-x22+x33-....y=log (1+x)ey=1+2x=ey-1 =y+y22+y33+....∞

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If $|x| < 1$ and $y = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots \dots \infty$ then $x =$

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$y - \frac{y^{2}}{2!} + \frac{y^{3}}{3!} + \dots \dots \infty$

$y - \frac{y^{2}}{2!} + \frac{y^{3}}{3!} - \dots \dots \infty$

$y + \frac{y^{2}}{2!} + \frac{y^{3}}{3!} + \dots \dots \infty$

answer is A.

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Detailed Solution

$\begin{array}{rcl} y & = & x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - . . . . \\ y & = & \log (1 + x) \\ e^{y} & = & 1 + 2 \\ x & = & e^{y} - 1 \\ = & y + \frac{y^{2}}{2} + \frac{y^{3}}{3} + . . . . \infty \end{array}$

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If x < 1 and y=x-x22+x33+x44+……∞ then x=

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If $|x| < 1$ and $y = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots \dots \infty$ then $x =$