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

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

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追问为什么要乘1/2？追答∵1/(2n-1)-1/(2n+1)
=[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=2/(2n-1)(2n+1)
多了2倍

1/(1*3)+1/(3*5)+1/(5*7)+.....+1/(29*31) = 15/31
n = 15

1/3+1/15+1/35+……+1/(2n-1)(2n+1)=15/31
1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)=15/31
(1/2)*[(1-1/3)+(1/5-1/7)+...+(1/(2n-1)-1/(2n+1))]=15/31
1-1/(2n+1)=30/31
2n/(2n+1)=30/31
所以2n=30
所以n=15
如果不懂，请追问，祝学习愉快！

1/3+1/15+1/35+1/63…+1/（2n-1）（2n+1）
=1/1x3+1/3x5+1/5x7+1/7x9…+1/（2n-1）（2n+1）
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+...+1/2(1/(2n-1)-1/(2n+1))
=1/2{1-1/(2n+1)}
=n/(2n+1)
n=15
同学你好，如果问题已解决，记得右上角采纳哦~~~您的采纳是对我的肯定~谢谢哦