1/3+1/15+1/35+……+1/(2n-1)(2n+1)=15/31,求n的值,

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/05 19:37:21

解
原式
=1/2(1-1/3)+1/2(1/3-1/5)+……+1/2[1/(2n-1)-1/(2n+1)]
=1/2[1+(1/3-1/3)+(1/5-1/5)+……+1/(2n-1)-1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=1/2×(2n/2n+1)
=n/(2n+1)=15/31
∴15(2n+1)=31n
∴30n+15=31n
∴n=15
再问：为什么要乘1/2？
再答： ∵1/(2n-1)-1/(2n+1)
=[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=2/(2n-1)(2n+1)
多了2倍

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