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问题: 数列

已知:f(n)=[1/(n+1)]+[1/(n+2)]+...+[1/(2n)]
求: f(n+1)-f(n)

解答:

f(n+1)-f(n)=[1/(n+2)+1/(n+3)+...+1/(2n+2)] -[1/(n+1)+1/(n+2)+...+1/(2n)]=[ 1/(n+1)]-1/(2n+1)-1/(2n+2)