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1/1*2+1/2*3+1/3*4+1/4*5+……+1/19*20=1990/1990*1991+1990/1991*1992+……+1990/1999*2000=
题目详情
1/1*2+1/2*3+1/3*4+1/4*5+……+1/19*20=
1990/1990*1991+1990/1991*1992+……+1990/1999*2000=
1990/1990*1991+1990/1991*1992+……+1990/1999*2000=
▼优质解答
答案和解析
1/1*2=1/1-1/2
1/2*3=1/2-1/3
.
1/1*2+1/2*3+1/3*4+1/4*5+……+1/19*20=
=1-1/20
=19/20
1990/1990*1991+1990/1991*1992+……+1990/1999*2000
=1990(1/1990-1/2000)
=1990*1/1990-1990*1/2000
=1-1990/2000
=1/200
1/2*3=1/2-1/3
.
1/1*2+1/2*3+1/3*4+1/4*5+……+1/19*20=
=1-1/20
=19/20
1990/1990*1991+1990/1991*1992+……+1990/1999*2000
=1990(1/1990-1/2000)
=1990*1/1990-1990*1/2000
=1-1990/2000
=1/200
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