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The sum of first n terms of the series a...

The sum of first n terms of the series `a + ar + ar^(2) +…+ ar^(n-1) +… oo` is -

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The sum of first r terms of a series is ar^(2) + br , find the first and 12th terms of the series.

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Knowledge Check

  • If the sum of the first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is (a)/(1-r) , then -

    A
    `-1 lt r lt 1`
    B
    `-1 le r lt 1`
    C
    `-1 lt r le 1`
    D
    `-1 le r le 1`

  • The sum of first n terms of the series 1^(2)+ 2 . 2^(2) + 3^(2) + 2. 4 ^(2) + 5^(2) +… is n/2 (n+1) ^(2) when n is even , When n is odd then the sum will be-

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

  • The sum to n terms of the series [1. (1!)+2. (2!)+ 3.(3!)+…] is-

    A
    `(n-1) !-1`
    B
    `(n-1)!+1`
    C
    `(n+1) !-1`
    D
    `(n+1) !-1`

    • Similar Questions

    Explore conceptually related problems

    If the sum of first n terms of a series is 2n^(2) + 3n , find the series.

    The sum of first n terms of a series is n^(2) + an + b . Show that b = 0 and the series is in A.P.

    Find the sum of first n terms of the following series : 1.2^(2) + 2.3^(2) + 3.4^(2)+…

    The sum of first n terms of a series is 3^(n)(a+b) when a, b are constants. Then the terms of the series are in

    Find the G.M. of n observations a, ar, ar^2..., ar^(n-1)

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