谁帮我证明一下n趋于无穷时(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)的极限等于零?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/26 10:14:22
谁帮我证明一下n趋于无穷时(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)的极限等于零?
![谁帮我证明一下n趋于无穷时(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)的极限等于零?](/uploads/image/z/932502-30-2.jpg?t=%E8%B0%81%E5%B8%AE%E6%88%91%E8%AF%81%E6%98%8E%E4%B8%80%E4%B8%8Bn%E8%B6%8B%E4%BA%8E%E6%97%A0%E7%A9%B7%E6%97%B6%EF%BC%88n%2B1%EF%BC%89%5E%EF%BC%88-3%2F2%EF%BC%89%2B%28n%2B2%29%5E%28-3%2F2%29%2B.%2B%282n%29%5E%28-3%2F2%29%E7%9A%84%E6%9E%81%E9%99%90%E7%AD%89%E4%BA%8E%E9%9B%B6%3F)
证明:
易知(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)>0,n>0.
x^(-3/2)是个减函数,(n+1)^(-3/2)最大.则(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)
易知(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)>0,n>0.
x^(-3/2)是个减函数,(n+1)^(-3/2)最大.则(n+1)^(-3/2)+(n+2)^(-3/2)+.+(2n)^(-3/2)
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