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有关分数的计算题（1/2-1/4+1/6-1/8+1/10-1/12+……+1/198-1/200）÷（1/51+1/52+1/53+……+1/100)=
题目详情
有关分数的计算题
（1/2 - 1/4 + 1/6 - 1/8 + 1/10 - 1/12 +……+ 1/198 - 1/200）÷ （1/51 + 1/52 + 1/53 + …… +1/100)=
（1/2 - 1/4 + 1/6 - 1/8 + 1/10 - 1/12 +……+ 1/198 - 1/200）÷ （1/51 + 1/52 + 1/53 + …… +1/100)=
▼优质解答
答案和解析
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
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