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The sum of n terms of the series (1)/(1...

The sum of n terms of the series ` (1)/(1 + x) + (2)/(1 + x^(2)) + (4)/(1 + x^(4)) + ………` is

A

`(1)/(x-1) + (k)/(x^(k) -1) , k = 2^(n)`

B

`(1)/(x-1) - (k)/(x^(k) -1) , k = 2^(n)`

C

`(1)/(x-1) + (k)/(x^(k -1) ) , k = 2^(n)`

D

`(1)/(x-1) -(k)/(x^(k -1)) , k = 2^(n)`

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Knowledge Check

  • The sum of n terms of the series sum_(x=1)^n"log "2^x/(3^(x-1) is

    A
    `"log"(2^(n-1)/3^(n+1))^n//2`
    B
    `"log"(2^(n+1)/3^(n-1))^n//2`
    C
    `"log"(3^(n-1)/2^(n+1))^n//2`
    D
    `"log"(3^(n+1)/2^(n-1))^n//2`

  • The sum of n terms of the series sum_(x=1)^n"log "2^x/(3^(x-1) is

    A
    `"log"(2^(n-1)/3^(n+1))^n//2`
    B
    `"log"(2^(n+1)/3^(n-1))^n//2`
    C
    `"log"(3^(n-1)/2^(n+1))^n//2`
    D
    `"log"(3^(n+1)/2^(n-1))^n//2`