1/2*3+1/3*4+1/4*5+1/5*6.+1/19*20
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1/2*3+1/3*4+1/4*5+1/5*6.+1/19*20
1/2*3+1/3*4+1/4*5+1/5*6.+1/19*20
1/2*3+1/3*4+1/4*5+1/5*6.+1/19*20
1/2*3+1/3*4+1/4*5+1/5*6.+1/19*20
=1/2-1/3+1/3-1/4+...+1/19-1/20
=1/2-1/20
=9/20
1-1/20=19/20