1/1*2+1/2*3+1/3*4...1/19*20=?

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1/1*2+1/2*3+1/3*4...1/19*20=?
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1/1*2+1/2*3+1/3*4...1/19*20=?
1/1*2+1/2*3+1/3*4...1/19*20=?

1/1*2+1/2*3+1/3*4...1/19*20=?
1/1*2+1/2*3+1/3*4...1/19*20=1-1/20=19/20

1/1*2+1/2*3+1/3*4...1/19*20
原式=1-1/2+1/2-1/3+........+1/19-1/20
中间的抵消
=1-1/20
=19/20