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Question: If \(y = x - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - \frac{x^{4}}{4!} + ......,\) then \(x =\)...

If y=x−x22!+x33!−x44!+......,y = x - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - \frac{x^{4}}{4!} + ......, then x=x =

A

log⁡e(1−y)\log_{e}(1 - y)

B

1log⁡e(1−y)\frac{1}{\log_{e}(1 - y)}

C

log⁡e11−y\log_{e}\frac{1}{1 - y}

D

log⁡e(1+y)\log_{e}(1 + y)

Answer

log⁡e11−y\log_{e}\frac{1}{1 - y}

Explanation

Solution

ex−ex+1\frac{e^{x} - e}{x + 1}

ex−ex−1\frac{e^{x} - e}{x - 1}.