Could you please tell where does this series converge to?

$sum_{k=1}^n ncdot((n!/(n-k+1)!cdot(k-1)!))$

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Where is the backslash on my keyboard?

I have a swiss keyboard (qwertz) for the franch language. All of my past computers had a backslash symbol on their keyboards, but for some reason, this one doesn’t. As copying and pasting backslashes in latex is really inefficient, I would like to know whether there is a hidden backslash on my keyboard, and, if not, how to create a backslash entry.

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What is NaN and where use it?

What is NaN and where use it?


Example 1:

perl -le 'print "Not the same!" unless "NaN" == "NaN"'

Not the same!


Example 2:

perl -le 'print "Not the same!" unless "undef" == "undef"'

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Other ways to find the formula of a general term of the sequence $x_{n+1} = frac{1}{2-x_n}$ where $x_1 = {1 over 2}$

Given a sequence:

$$
x_{n+1} = frac{1}{2-x_n}
$$
Finding the general form of the sequence $x_n$ where $x_1 = {1 over 2}$ and $n in mathbb N$

What I’ve done is expand the terms $n$ times and then go backwards in order to find some pattern, so:

$$
x_{n+1} = frac{1}{2 – x_n} = frac{1}{2-frac{1}{2-x_{n-1}}} = dots
$$

Now wrapping from the bottom:

$$
frac{1}{2 – {1 over 2}} = {2 over 3} \
frac{1}{2 – {2 over 3}} = {3 over 4} \
dots \
{1 over {2 – frac{n-1}{n}}} = {n over n+1}
$$

So the pattern suggests that $x_n = {n over n+1}$.

I’m not satisfied with that approach since i believe it’s going to fail for more complicated sequences.

What approach or technique could i use to reach the same result in a more “analytical” way?

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Show that ${y in M : ||x-y||<1}=C$ where $C$ is the closed ball around $x$ with radius 1

Let $(M,||cdot||)$ be a normed vectorspace and $x in M$.

Show that ${y in M : ||x-y||<1}=text{int}(C)$ where $C$ is the closed ball around $x$ with radius 1, that is ${y in M: d(x,y) leq1}$.

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Permutation of multiple sets of elements where adjacent elements are different.

There are 5 red balls, 6 white balls and 7 black balls. How many ways can we arrange these ball in a line where the adjacent balls are in different color? And generalize the 5, 6, 7 into R, W, B.

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Where are gnome-terminal profiles stored on a Linux distribution?

I have used (Red Hat, Ubuntu, CentOS, others). These distributions utilize Gnome-terminal, and provide flexible ways to set up different terminal profiles via a drop down menu located in the terminal window, directly above where commands are, usually, entered. These profiles allow making changes to the font and color properties of different files etc..

Where are these different profiles for the terminal stored?

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Where did Jake Chambers come from?

I recently ended reading The Dark Tower series, and I got a doubt. Warning for spoilers of several books.


It is stated that the one that dies in the key world is permanently dead and cannot wake up in another reality. In the first book, The Gunslinger

In the second book, The Drawing of the Three, we find out that the man that killed

was the same that threw a brick on Susannah’s head when she was a child and the same that pushed her in the rails when she was young. So, to me,

and Susannah came from the same world. Eddie didn’t came from their world because in his reality Co-Op city is in Brooklin, but in the real world is in Bronx.

We know that Susannah came from the key world because Moses Carver, her godfather, was the last of Tet Corp. alive when Rolland went to the key world for the last time. And he missed Susannah, that has disappeared in that world.

The question is, Jake was really from the Key World? And if yes,

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From where did Jake Chambers come from?

I recently ended reading The Dark Tower series, and I got a doubt. Warning for spoilers of several books.


It is stated that the one that dies in the key world is permanently dead and cannot wake up in another reality. In the first book, The Gunslinger

In the second book, The Drawing of the Three, we find out that the man that killed

was the same that threw a brick on Susannah’s head when she was a child and the same that pushed her in the rails when she was young. So, to me,

and Susannah came from the same world. Eddie didn’t came from their world because in his reality Co-Op city is in Brooklin, but in the real world is in Bronx.

We know that Susannah came from the key world because Moses Carver, her godfather, was the last of Tet Corp. alive when Rolland went to the key world for the last time. And he missed Susannah, that has disappeared in that world.

The question is, Jake was really from the Key World? And if yes,

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Closing out a Short Guts position where the put side has 0 volume and 0 OI

This spread may not even be available after the holiday is over, but here’s my question:

I found a high paying high probability guts trade. If you don’t know, a short guts is selling an ITM put and an ITM call. The money is made off the premium and as long as the stock price remains between the call and put at expiration there’s no loss. In the trade I’m considering there’s something like a 90% chance of break even or better and a damn good chance of very good profit – but how do I close the trade and make money before expiration? Or if the stock starts to slip away from me? And what’s going to happen to the value of the contract from my perspective as expiration approaches?

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