Question

计算100^2-99^2-98^2-97^2-96^2-95^2+……+2^2-1^2

Answer 1

原式=(100-99)(100+99)+(98-97)(98+97)+……+(2-1)(2+1)
=1*(100+99)+1*(98+97)+……+1*(2+1)
=100+99+98+97+……+2+2
=(100+1)+(99+2)+……+(51+50)
=101+101+……+101
=101*50
=5050

Answer 2

100^2-99^2-98^2-97^2-96^2-95^2+……+2^2-1^2
=100^2-(99^2+98^2+97^2+96^2+95^2+……+2^2+1^2)
=100^2-99*100*199/ 6
=-318350