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The sum of the first n terms of the seri...

The sum of the first n terms of the series `1/2 +3/4 +7/8 +(15)/(16)+… is `

A

`2^n -n -1`

B

`1-2^(-2)`

C

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

D

`2^n -1`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The sum of the first 10 terms of the series 9+99+999 +…. is

    A
    `9/8 (9^(10) -1)`
    B
    `(100)/9 (10^9 -1)`
    C
    `10^9 -1`
    D
    `(100)/9 (10^(10) -1)`

  • The sum of the first five terms of the series 3+4 1/2 +6 3/4 +…..will be

    A
    `39 9/(16)`
    B
    `18 3/(16)`
    C
    `39 7/(16)`
    D
    `13 9/(16)`

  • If the sum of the first ten terms of the series (1 3/5)^2 +(2 2/5)^2 +(3(1/5)^2 +4^2 +(4 4/5)^2 +…IS (16)/5 m, then m is equal to :

    A
    101
    B
    100
    C
    99
    D
    102

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