L******k 发帖数: 33825 | 1 Prove: for n 大于等3,n 是自然数
1/(n+1)+1/(n+2)+1/(n+3)+....+1/(2n)>3/5 |
d*j 发帖数: 13780 | 2 Prove: for n 大于等3,n 是自然数
f(n) = 1/(n+1)+1/(n+2)+1/(n+3)+....+1/(2n) 是个严格增函数, strictly inc
reasing
when n=3, f(3) = 1/4 + 1/5 + 1/6 > 3/5
for any n > 3, f(n) > f(3), 因为是单调递增函数
好了
【在 L******k 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Prove: for n 大于等3,n 是自然数 : 1/(n+1)+1/(n+2)+1/(n+3)+....+1/(2n)>3/5
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L******k 发帖数: 33825 | 3 谢谢啊 那和3/5有什么关系啊?
inc
【在 d*j 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Prove: for n 大于等3,n 是自然数 : f(n) = 1/(n+1)+1/(n+2)+1/(n+3)+....+1/(2n) 是个严格增函数, strictly inc : reasing : when n=3, f(3) = 1/4 + 1/5 + 1/6 > 3/5 : for any n > 3, f(n) > f(3), 因为是单调递增函数 : 好了
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d*j 发帖数: 13780 | 4 没什么关系吧。。。。 就是 n=3的时候, 凑了一个数
使得 10/24 > 10/25
我觉得
呵呵
【在 L******k 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 谢谢啊 那和3/5有什么关系啊? : : inc
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m****s 发帖数: 8992 | 5 You can set up induction really easily and naturally on this
The last point to prove is 1/(2n+1) - 1/2(n+1) > 0. When n > 3
Which is obvious. |
L******k 发帖数: 33825 | 6 最后一步没看懂!
assume P(n) is true,want to show that P(n+1) is true
右边是3/5 怎么写n+1项啊!?
【在 m****s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : You can set up induction really easily and naturally on this : The last point to prove is 1/(2n+1) - 1/2(n+1) > 0. When n > 3 : Which is obvious.
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m****s 发帖数: 8992 | 7 P(n+1)-P(n)
You will see equal to what I said as the last step
It's positive. Doesn't even need the right hand side.
QED
【在 L******k 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 最后一步没看懂! : assume P(n) is true,want to show that P(n+1) is true : 右边是3/5 怎么写n+1项啊!?
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L******k 发帖数: 33825 | 8 好的 理解了!!
谢谢了啊~~
我就是一直在纠结 RHS!!
【在 m****s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : P(n+1)-P(n) : You will see equal to what I said as the last step : It's positive. Doesn't even need the right hand side. : QED
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