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Question: In the expansion of \(2\log_{e}x - \log_{e}(x + 1) - \log_{e}(x - 1)\), the coefficient of \(x^{- 4}...

In the expansion of 2log⁡ex−log⁡e(x+1)−log⁡e(x−1)2\log_{e}x - \log_{e}(x + 1) - \log_{e}(x - 1), the coefficient of x−4x^{- 4} is.

A

1/2

B

−1- 1

C

1

D

None of these

Answer

1/2

Explanation

Solution

−1- 1

1+13!+15!+17!+.....∞=e1 + \frac{1}{3!} + \frac{1}{5!} + \frac{1}{7!} + .....\infty = e

e+e−12\frac{e + e^{- 1}}{2}

The coefficient of e−e−12\frac{e - e^{- 1}}{2}.