2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?

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2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?2/1*3+2/3*5+2/5*7+.+2/17*1

2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?
2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?

2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21=?
2/1*3+2/3*5+2/5*7+.+2/17*19+2/19*21
=1-1/3+1/3-1/5+1/5-1/7+..+1/17-1/19+1/19-1/21
=1-1/21
=20/21

2/1*3+2/3*5+2/5*7+......+2/17*19+2/19*21
=1-1/3+1/3-...+1/19-1/21
=20/21
谢谢采纳···

2/1*3=1-1/3
2/3*5=1/3-1/5
2/5*7=1/5-1/7
......
2/19*21=1/19-1/21
所以
2/3*5+2/5*7+......+2/17*19+2/19*21
=1-1/3+1/3-1/5+1/5-1/7+...+1/19-1/21
=1-1/21
=20/21

20/21