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1.1/1*2+1/2*3+1/3*4+……+1/n(n+1) 2.1/1*3+1/3*5+1/5*7+……+1/(2n-1)*(2n+1)

分类: 作业答案 • 2022-05-08 19:54:26
问题描述：

1.1/1*2+1/2*3+1/3*4+……+1/n(n+1) 2.1/1*3+1/3*5+1/5*7+……+1/(2n-1)*(2n+1)

答

1.1/1*2+1/2*3+1/3*4+……+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/1*3+1/3*5+1/5*7+……+1/(2n-1)*(2n+1)
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+.+1/2*[1/(2n-1)-1/(2n+1)]
=1/2*[1-1/3+1/3-1/5+1/5-1/7+.+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=1/2*2n/(2n+1)
=n/(2n+1)

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