求1\19×21+1\21×23+1\23×25+.+1\97×99的值急
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![求1\19×21+1\21×23+1\23×25+.+1\97×99的值急](/uploads/image/z/70071-15-1.jpg?t=%E6%B1%821%5C19%C3%9721%EF%BC%8B1%5C21%C3%9723%EF%BC%8B1%5C23%C3%9725%EF%BC%8B.%EF%BC%8B1%5C97%C3%9799%E7%9A%84%E5%80%BC%E6%80%A5)
求1\19×21+1\21×23+1\23×25+.+1\97×99的值急
求1\19×21+1\21×23+1\23×25+.+1\97×99的值
急
求1\19×21+1\21×23+1\23×25+.+1\97×99的值急
1/n(n+2)=[1/n-1/(n+2)]*1/2
1/19*21+1/21*23+----+1/97*99
=1/2*(1/19-1/21+1/21-1/23+1/23-1/25+-----+1/97-1/99)
=1/2*(1/19-1/99)
=40/1881