1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?要简便运算

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1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?要简便运算

1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?要简便运算
1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?
要简便运算

1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?要简便运算
1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+.+1/2*(1/17-1/19)+1/2*(1/19-1/21)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/17-1/19+1/19-1/21)
=1/2*(1-1/21)
=1/2*20/21
=10/21