100^2 - 99^2 + 98^2 - 97^2 + .+ 2^2 - 1^2
= (100^2 - 99^2) + (98^2 - 97^2) + .+ (2^2 - 1^2)
= (100 + 99)*(100 - 99) + (98 + 97)(98 - 97) + ...+ (2 + 1)(2 - 1)
= 100 + 99 + 98 + 97 + ...+ 2 + 1
= (100 + 1)*50
= 5050