The 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 isClass: 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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