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2/15+2/35+2/63+2/99+2/143=?1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)=?
题目详情
2/15+2/35+2/63+2/99+2/143=?
1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)=?
1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)=?
▼优质解答
答案和解析
2/15+2/35+2/63+2/99+2/143
=(1/3-1/5)+(1/5-1/7)+(1/7+1/9)+(1/9-1/11)+(1/11-1/13)
=1/3-1/5+1/5-1/7+1/7+1/9+1/9-1/11+1/11-1/13
=1/3-1/13
=10/39
1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)
=1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1-1/2+1/10
=3/5
=(1/3-1/5)+(1/5-1/7)+(1/7+1/9)+(1/9-1/11)+(1/11-1/13)
=1/3-1/5+1/5-1/7+1/7+1/9+1/9-1/11+1/11-1/13
=1/3-1/13
=10/39
1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)
=1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1-1/2+1/10
=3/5
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