已知n€N且n>1,用放缩法证明:1+1/根号2+1/根号3+…+1/根号n>根号n.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 16:13:37
![已知n€N且n>1,用放缩法证明:1+1/根号2+1/根号3+…+1/根号n>根号n.](/uploads/image/z/2624376-48-6.jpg?t=%E5%B7%B2%E7%9F%A5n%26%238364%3BN%E4%B8%94n%3E1%2C%E7%94%A8%E6%94%BE%E7%BC%A9%E6%B3%95%E8%AF%81%E6%98%8E%EF%BC%9A1%2B1%2F%E6%A0%B9%E5%8F%B72%2B1%2F%E6%A0%B9%E5%8F%B73%2B%E2%80%A6%2B1%2F%E6%A0%B9%E5%8F%B7n%3E%E6%A0%B9%E5%8F%B7n.)
已知n€N且n>1,用放缩法证明:1+1/根号2+1/根号3+…+1/根号n>根号n.
已知n€N且n>1,用放缩法证明:1+1/根号2+1/根号3+…+1/根号n>根号n.
已知n€N且n>1,用放缩法证明:1+1/根号2+1/根号3+…+1/根号n>根号n.
因为1>1/√2>1/√3>…>1/√n
所以
1+1/√2+1/√3+…+1/√n >n*(1/√n)=√n