1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
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![1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100](/uploads/image/z/2508416-8-6.jpg?t=1%2F1%C3%972%2B1%2F2%C3%973%2B1%2F3%C3%974%2B.%2B1%2F98%C3%9799%2B1%2F99%C3%97100)
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1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=(1-1/100)
=99/100