Question

计算题100^2-99^2+98^2-97^2+.+2^2-1^2

Answer 1

100^2-99^2+98^2-97^2+.+2^2-1^2

=(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+1

=(100+1)+...(50+51)

=101*50

=5050