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Sequence & Series Test - 5
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Sequence & Series Test - 5

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  • Question 1/10
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    Suppose a, b and c are positive real numbers satisfying the system of equations

    (a2 + ab + b2) (b2 + bc + c2) (c2 + ca + a2) = abc

    (a4 + a2b2 + b4) (b4 + b2c2 + c4) (c4 + c2a2 + a4) = a3b3c3.

    Then,

    Solutions

     

  • Question 2/10
    1 / -0

    Solutions

    = T1 - T2 + T3 -T4 + ........∞

    = (1 - ½) - (1/2 - 1/3) + (1/3 - ¼) - (1/4 - 1/5) + ....... ∞

    = 2 (1 -½ + 1/3 - ¼ + .....) - 1 = 2 log (1 + 1) - loge e = loge (4/e)

    S = loge(4/e)

    eS = 4/e

     

  • Question 3/10
    1 / -0

     

    The sum up to infinity of the series 1 + 2 

    Solutions

     

  • Question 4/10
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    The sum upto n terms of the series 1.3.5 + 3.5.7 + 5.7.9 + ...... is

    Solutions

    The rth term of the series is given by tr = (2r - 1) (2r + 1) (2r + 3) = 8r3 + 12r2 - 2r - 3

    Therefore, sn, the sum to n terms of the series is given by

     

  • Question 5/10
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    The coefficient of xn in the series 1 

    Solutions

     

  • Question 6/10
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    If a, b, c are in AP, then 

    Solutions

     

  • Question 7/10
    1 / -0

    If the sum of first n terms of an A.P. is cn2, then the sum of squares of these n terms is

    Solutions

     

  • Question 8/10
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    The sum to infinity of the series  

    Solutions

     

  • Question 9/10
    1 / -0

    Solutions

     

  • Question 10/10
    1 / -0

    Suppose a2, b2, c2 are in A.P.

    Statement – 2: b + c, c + a, a + b are in H.P.

    Solutions

     

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