麻烦各位帮我看看这道题第二小题哪里错了 数列求和 错位相减法
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/22 18:58:03
麻烦各位帮我看看这道题第二小题哪里错了 数列求和 错位相减法
![](http://img.wesiedu.com/upload/c/5e/c5ee5bde04e0806d6e99a2f958ec6fac.jpg)
![](http://img.wesiedu.com/upload/c/5e/c5ee5bde04e0806d6e99a2f958ec6fac.jpg)
![麻烦各位帮我看看这道题第二小题哪里错了 数列求和 错位相减法](/uploads/image/z/3984758-62-8.jpg?t=%E9%BA%BB%E7%83%A6%E5%90%84%E4%BD%8D%E5%B8%AE%E6%88%91%E7%9C%8B%E7%9C%8B%E8%BF%99%E9%81%93%E9%A2%98%E7%AC%AC%E4%BA%8C%E5%B0%8F%E9%A2%98%E5%93%AA%E9%87%8C%E9%94%99%E4%BA%86+%E6%95%B0%E5%88%97%E6%B1%82%E5%92%8C+%E9%94%99%E4%BD%8D%E7%9B%B8%E5%87%8F%E6%B3%95)
错位相减时错了:
1/2Tn=(1/2)^(-1)+2*[(1/2)^0+(1/2)^1+(1/2)^2+...+(1/2)^(n-2)]-(2n-1)*(1/2)^(n-1)
=2+2*[1-(1/2)^(n-1)]/(1-1/2)-(2n-1)*(1/2)^(n-1)
=2+4-4*-4*(1/2)^(n-1)-(2n-1)*(1/2)^(n-1)
=6-(2n+3)*(1/2)^(n-1)
Tn=12-(2n+3)*(1/2)^(n-2)
1/2Tn=(1/2)^(-1)+2*[(1/2)^0+(1/2)^1+(1/2)^2+...+(1/2)^(n-2)]-(2n-1)*(1/2)^(n-1)
=2+2*[1-(1/2)^(n-1)]/(1-1/2)-(2n-1)*(1/2)^(n-1)
=2+4-4*-4*(1/2)^(n-1)-(2n-1)*(1/2)^(n-1)
=6-(2n+3)*(1/2)^(n-1)
Tn=12-(2n+3)*(1/2)^(n-2)