观察下列等式,1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-4/1;……1/1×2+1/2×3+1/3×4+1/4×5=1/1*3+1/3*5+1/5*7……+1/(2n-1)(2n+1)=17/35求n的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 15:36:53
![观察下列等式,1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-4/1;……1/1×2+1/2×3+1/3×4+1/4×5=1/1*3+1/3*5+1/5*7……+1/(2n-1)(2n+1)=17/35求n的值](/uploads/image/z/5430186-18-6.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%2C1%2F1%2A2%3D1-1%2F2%EF%BC%9B1%2F2%2A3%3D1%2F2-1%2F3%EF%BC%9B1%2F3%2A4%3D1%2F3-4%2F1%EF%BC%9B%E2%80%A6%E2%80%A61%2F1%C3%972%2B1%2F2%C3%973%2B1%2F3%C3%974%2B1%2F4%C3%975%3D1%2F1%2A3%2B1%2F3%2A5%2B1%2F5%2A7%E2%80%A6%E2%80%A6%2B1%2F%EF%BC%882n-1%29%282n%2B1%29%3D17%2F35%E6%B1%82n%E7%9A%84%E5%80%BC)
观察下列等式,1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-4/1;……1/1×2+1/2×3+1/3×4+1/4×5=1/1*3+1/3*5+1/5*7……+1/(2n-1)(2n+1)=17/35求n的值
观察下列等式,
1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-4/1;……
1/1×2+1/2×3+1/3×4+1/4×5=
1/1*3+1/3*5+1/5*7……+1/(2n-1)(2n+1)=17/35求n的值
观察下列等式,1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-4/1;……1/1×2+1/2×3+1/3×4+1/4×5=1/1*3+1/3*5+1/5*7……+1/(2n-1)(2n+1)=17/35求n的值
1/1×2+1/2×3+1/3×4+1/4×5=1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)=1-1/5=4/5
1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)
=1/3+1/2*(1/3-1/5)+1/2(1/5-1/7)+……+1/2*[1/(2n-1)-1/(2n+1) ]
=1/3+1/2[1/3-1/5+1/5-1/7+……+(2n-1)-1/(2n+1)]
=1/3+1/2[1/3-]
=1/2-1/(2n+1)
=17/35
解得 n=34