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  4. The value of the sum 112-12+122-22+132-32+ ldots ldots .+202-102 equals

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Q. The value of the sum $11^2-1^2+12^2-2^2+13^2-3^2+\ldots \ldots .+20^2-10^2$ equals

Sequences and Series

Solution:

$S=\displaystyle\sum_{n=1}^{10}(n+10)^2-n^2=\displaystyle\sum_{n=1}^{10}(100+20 n)=1000+20\left(\frac{10 \cdot 11}{2}\right)=100(10+11)=2100$