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Thread: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

  1. #1
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    (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    Find the values of

    (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50).

    -- James


  2. #2
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    Re: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    The ans is 1/50


  3. #3
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    Re: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    (1/2)-(1/6)-(1/12).......-(1/2450)
    -1/2(-1+1/3+1/6......+1/1275)----taking the reciprocal
    -2(-1+3+6+......1275)---then by using Arithmetic progression we can calculate it.


  4. #4
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    Re: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    @ TigerElango
    U need not complicate it so much.. [BTW i would be surprised if you arrive at the ans in your approach]
    Here is a simpler approach
    Split every term as follows
    1/1.2 = 1/1 - 1/2
    1/2.3 = 1/2 - 1/3
    ...
    ...
    1/49.50 = 1/49 - 1/50

    If you do so and then cancel out the terms.. you will see that only
    1/50 remains.


  5. #5
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    Re: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    sundar give a wounderful explanation.....

    nice keep it up...


  6. #6
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    Re: (1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

    Sundar,
    I really appreciate the way you solved this problem. The Perfect approach to attack this problem. Hats off to u man

    Last edited by jamesravid; 11-08-2006 at 11:28 PM.

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