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(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+.......

`(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....`

A

`log_(e )2`

B

`log_(e )3`

C

`log_(e )5`

D

`log_(e )2-(1)/(2)`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • (1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……oo=

    A
    `1+log_(e )2`
    B
    `1-log_(e )2`
    C
    `(1)/(2)-log_(e )2`
    D
    `log_(e )2`

  • The sum of the series (1)/(1.3.5)+(1)/(3.5.7)+(1)/(5.7.9)+... is

    A
    `3 log_(e)x`
    B
    `1//8`
    C
    `1//9`
    D
    `1//12`

  • Sum of the series (1)/(4.5.6)+(1)/(5.6.7)+(1)/(6.7.8)+... upto oo is

    A
    `(1)/(20)log_(e)e`
    B
    `(1)/(10)log_(e)e`
    C
    `(1)/(40)log_(e)e`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    (1)/(1.2)+(1)/(3.4)+(1)/(5.6)+…..oo=

    (1)/(2.3)+(1)/(4.5)+(1)/(6.7)+(1)/(8.9)+...

    (1)/(1.3)+(1)/(2)((1)/(3.5))+(1)/(3)((1)/(5.7))+....=

    (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

    If S=(1)/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...."to "oo , then S =

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