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FalseCan not import an old (draft) version of RIFOText. Can only import versions created after version 4.3: 2016 Trial version – will not be renewed.Q:
Is $1 + \frac{1}{n}$ necessarily monotonically increasing?
I’ve been doing some thinking in order to solve a problem and it occurred to me that the sequence $1 + \frac{1}{n}$ may or may not be monotonically increasing. I thought that the argument was simple but I have come to a dead end. My work for the day is this:
$$
1 + \frac{1}{n} > 1 + \frac{2}{n} >… > 1 + \frac{n}{n} = 1
$$
Therefore, by the principle of mathematical induction, it is indeed true that $1 + \frac{1}{n} > 1 + \frac{2}{n} >… > 1 + \frac{n}{n}$. However, there does not seem to be any way to extend that argument to show that $1 + \frac{1}{n} > \frac{1}{n}$ or, in other words, that $1 + \frac{1}{n}$ is monotonically increasing.
A:
We know that $\displaystyle \lim_{n\to \infty} (1+\frac{1}{n})=1$.
It seems that you want to show that this sequence is increasing.
You can do that if you observe that $1+\frac{1}{n}\geq 1+\frac{1}{2n}$
and thus $1+\frac{1}{n}-\frac{1}{2n}=\frac{1}{2n}\geq 0$
1. Field of the Invention
The present invention relates generally to an electrical connector, and more particularly to a card edge connector mounted on a PCB.
2. Description of Related Arts
U.S. Pat. No. 7,022,941 to Charles et al. issued Apr. 4, 2006 discloses a card edge connector. The card edge connector comprises a housing, a plurality of contacts retained in the housing, an insulation body partially covers the contacts, and a frame partially covers the contacts. The insulation body, the frame, and the contacts are molded to form a solid structure. The contact has a connecting portion. The contacts are stamped from a metal strip. Each contact has a contact portion which is stamped from a contact portion of the metal strip. The contact portion is a plate-like structure, and has a receiving cavity. The contact portion has a contact part of contacting with the PCB. A spring is received in the receiving cavity, and the spring abuts against the PCB. When the PCB is inserted into the housing
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