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The sum to n terms of the series 1/2 + 3...

The sum to `n` terms of the series `1/2 + 3/4 + 7/8 + 15/16 + .......` is

A

`n - 1 + 2^(-n)`

B

1

C

`n - 1`

D

`1 + 2^(-n)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The sum to n terms of the series 4/3 + 10/9 + 28/27 + ……. is

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

  • If the sum of n terms of the series 2^(3) + 4^(3) + 6^(3) + ......... is 3528 then n =

    A
    10
    B
    6
    C
    8
    D
    9

  • The sum to n terms of the series 1 + (1 + 3) + (1 + 3 + 9) + (1 + 3 + 9 + 27)+ .......... is

    A
    `(3(3^(n) - 1))/4 - 1`
    B
    `(3(3^(n) - 1) - 2n)/4`
    C
    `(3(3^(n) - 1) - n)/4`
    D
    `(2n - 3(3^(n) - n))/4`

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