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The sum of the series 1+3/2+7/4+15/8+3...

The sum of the series
`1+3/2+7/4+15/8+31/16+…` upto n terms is equal to

A

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

B

`2-1/2^n`

C

`2+1/2^n`

D

`2n-1+1/2^n`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Sum of the series 1 + 3 + 7 + 15 + 31 +… to n terms is

    A
    `2^(n) - 2 - n`
    B
    `2^(n + 1) + 2 + n`
    C
    `2^(n + 1) - 2 - n`
    D
    none

  • The sum of the series 3+8+16+27+41 …………… upto 20 terms is equal to

    A
    4230
    B
    4430
    C
    4330
    D
    4500

  • Find the sum of the series 3 + 7 + 13 + 21 + 31 + … to n terms . Find the sun when n=20

    A
    `(n(n^(2) + 2n + 3))/(3), 3110`
    B
    `(n(n^(2) + 3n + 5))/(3), 3110`
    C
    `(n(n^(2) + 3n + 5))/(3) , 3120`
    D
    `(n(n^(2) + 2n +2))/(3), 3120`

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