1/1×2+1/2×3+1/3×4+.+1/9×10=

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1/1×2+1/2×3+1/3×4+.+1/9×10=

1/1×2+1/2×3+1/3×4+.+1/9×10=
1/1×2+1/2×3+1/3×4+.+1/9×10=

1/1×2+1/2×3+1/3×4+.+1/9×10=
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10