1/1*3+1/3*5+1/5*7...+1/17*19+1/19*21

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1/1*3+1/3*5+1/5*7...+1/17*19+1/19*211/1*3+1/3*5+1/5*7...+1/17*19+1/19*211/1*3+1/3*5+1/5*7...+1/17*19

1/1*3+1/3*5+1/5*7...+1/17*19+1/19*21
1/1*3+1/3*5+1/5*7...+1/17*19+1/19*21

1/1*3+1/3*5+1/5*7...+1/17*19+1/19*21
原式=1/2 (1/3-1/5+1/5-1/7+...+1/19-1/21)
=1/2 (1/3-1/21)
=1/2 ×6/21
=3/21
=1/7

1/1*3+1/3*5+1/5*7...+1/17*19+1/19*21
=(1/2)[1-1/3+1/3-1/5+...+1/19-1/21]
=(1/2)(1-1/21)
=10/21