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Sum of the first n terms of the series 1...

Sum of the first `n` terms of the series `1/2+3/4+7/8+(15)/(16)+.........` is equals to (a).`2^n+n-1` (b). `n-1+2^(-n)` (c). `n+2^(-n)-1` (d). `2^n+1`

A

`2^(n)+n-1`

B

`1-2^(-n)`

C

`n+26(-n)-1`

D

`26(n)-1`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • The sum to n terms of the series (1)/(2) + (3)/(4) + (7)/(8) + (15)/(16)+…. is equal to :

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

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