赞 毛毛雨和毛豆 幼苗
共回答了20个问题采纳率：90% 举报
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
=(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
1年前
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