Question

1951^2-1950^2+1953^2-1952^2+…+2011^2-2010^2

Answer 1

(n+1)²-n²=(n+1+n)(n+1-n)=2n+1

因此：1951^2-1950^2+1953^2-1952^2+…+2011^2-2010^2

=(2*1950+1)+(2*1952+1)+...+(2*2010+1)

=2(1950+1952+...+2010)+31

=2*(1950+2010)*31/2+31

=(1950+2010)*31+31

=122791