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  4. The sum of the products of the ten numbers ± 1, ± 2, ± 3, ± 4, ± 5 taking two at a time is

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Q. The sum of the products of the ten numbers $\pm 1, \pm 2, \pm 3, \pm 4, \pm 5$ taking two at a time is

Sequences and Series

Solution:

$\therefore \sum a b=\frac{1}{2}\left[\left(\sum a\right)^2-\sum a^2\right]$
$=\frac{1}{2}\left[(1-1+2-2+\ldots . .+5-5)^2-2\left(1^2+2^2+3^2+4^2+5^2\right)\right]$
$=\frac{1}{2}[0-110]=-55$