1*99+2*98+3*97+4*96+......+98*2+99*1
=[100-99]99+[100-98]*98+[100-97]97+...+[100-51]*51+50*50+[[100-51]*51+...+[100-99]*99
=[100*99-99^2+100*98-98^2+100*97-97^2+...+100*51-51^2]*2+50^2
=[100*(99+98+97+...+51)-(99^2+98^2+97^2+...+51^2)]*2+50^2
=[100*(99+51)*49/2-(99^2+98^2+97^2+...+51^2)]*2+50^2
99^2+98^2+...+51^2
=[99^2+98^2+...+1^2]-[50^2+49^2+...+1^2]
=99*[99+1][2*99+1]/6-50*[50+1][2*50+1]/6
=285425
所以上式=[100*3675-285425]*2+2500
=166650
