A square -b square =(a-b)(a+b)

Obviously, the original formula =

( 1949- 1950)( 1949+ 1950)+( 195 1- 1952)( 195 1+ 1952)+...........( 1999-2000)( 1999+2000)=

-( 1949+ 1950)-( 195 1+ 1952)-( 1953+ 1954)-.....( 1999+2000)

=- 1949+ 1950+ 195 1+ 1952+。 . . . 1999+2000

=-( 1949+2000)*26

Calculations are available.

The reason why the city is multiplied by 26 is that the sum of the first term and the last term is equal to the sum of the second term from 1949 to 2000***52, so the logarithm ***52/2=26 pairs.