MathematicsThe sum of the product of the 2n numbers ±1, ±2, ±3, … , ±n taking two at a time isClass: 10

The sum of the product of the 2n numbers ±1, ±2, ±3, … , ±n taking two at a time is


Class: 10


  1. A
    –∑ n2
  2. B
    1
  3. C
    0
  4. D
    None of these 

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    Solution:

    The series will be like:
    T1 = –1 × 1 = –1
    T2 = –2 × 2 = –22
    T3 = –3 × 3 = –32
    Tn = –n2
    Hence the series will be
    –1 –22 –32 – ⋯ –n2
    ⇒ –(1 +22 +32 + ⋯ +n2)
    Hence the general term will be Tn = –n2
    Therefore the sum of the series upto nth term will be
    ∑ Tn
    ⇒ –∑ n2
      
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