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The series expansion of log{(1+x)^(1+x)(...

The series expansion of `log{(1+x)^(1+x)(1-x)^(1-x)}` is

A

`2{(x^(2))/(1.2)+(x^(4))/(3.4)+(x^(6))/(5.6)+..}`

B

`{(x^(2))/(1.2)+(x^(4))/(3.4)+(x^(6))/(5.6)+..}`

C

`2{(x^(2))/(1.2)+(x^(4))/(2.3)+(x^(6))/(3.4)+..}`

D

none of these

Text Solution

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The correct Answer is:
a
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Knowledge Check

  • The coefficient of x^3 in the infinite series expansion of (2)/((1-x) (2-x) ) , for |x| lt 1 , is

    A
    `-1//16`
    B
    `15//8`
    C
    `-1//8`
    D
    `15//16`

  • The coefficient of x^(n) in the expansion of log_(e)((1)/(1+x+x^(2)+x^(3))) when is odd, is equal to

    A
    `-2//n`
    B
    `-1//n`
    C
    `1//n`
    D
    none of these

  • The coefficient of x^(n) in the expansion of log_(e)(1)/(1+x+x^(2)+x^(3)) when n is odd is

    A
    `(2)/(n)`
    B
    `-(1)/(n)`
    C
    `(1)/(n)`
    D
    `(2)/(n)`

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