1/1x1/2-1/2x1\3-1\3x1/4...1/99x1/100

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1/1x1/2-1/2x1\3-1\3x1/4...1/99x1/100
1/1x1/2-1/2x1\3-1\3x1/4...1/99x1/100

1/1x1/2-1/2x1\3-1\3x1/4...1/99x1/100
1/1x1/2-1/2x1\3-1\3x1/4...1/99x1/100
=1-1/2+1/2-1/3+...+1/99-1/100
=99/100