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计算1╱5×6+1╱6×7+1╱7×8+……+1╱18×19+1╱19×20

题目详情
计算1╱5×6+1╱6×7+1╱7×8+……+1╱18×19+1╱19×20
▼优质解答
答案和解析
1/5×6+1/6×7+1/7×8+……+1/18×19+1/19×20
=(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+……+(1/18-1/19)+(1/19-1/20)
=1/5-1/6+1/6-1/7+1/7-1/8+……+1/18-1/19+1/19-1/20
=1/5-1/20
=4/20-1/20
=3/20