Question

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

• A. 2010
• B. 2110
• C. 2100
• D. 2200

Answer 1

Answer: (C)

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