1/2-1/4+1/6-1/8+1/10-1/12+…+1/198-1/200

　　=(1-1/2+1/3-1/4+...+1/99-1/100)/2

　　=[(1+1/2+...+1/99+1/100)-2(1/2+1/4+...+1/98+1/100)]/2

　　=[(1+1/2+...+1/99+1/100)-(1+1/2+...+1/49+1/50)]/2

　　=(1/51+1/52+1/53+...+1/99+1/100)/2

　　所以原式

　　=(1/2)(1/51+1/52+1/53+...+1/99+1/100)/(1/51+1/52+1/53+…+1/100)

　　=1/2