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计 算 题（数学·2001年·四川省成都市成都七中）
(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×(1+1/4)×(1-1/4)×⋯×(1+1/99)×(1-1/99)
解答提示
原式=3/2×1/2×4/3×2/3×5/4×3/4×6/5×4/5×⋯×98/97×96/97×99/98×97/98×100/99×98/99
=1/2×100/99
=50/99
(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×(1+1/4)×(1-1/4)×⋯×(1+1/99)×(1-1/99)
原式=3/2×1/2×4/3×2/3×5/4×3/4×6/5×4/5×⋯×98/97×96/97×99/98×97/98×100/99×98/99
=1/2×100/99
=50/99