# Tagged Questions

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### what is the coefficient of following expression

what is the co-efficient of $x^{50}$ in the expansion of $$\frac{1}{(1-x^{1.7})(1-x^{1.8})(1-x^{2.6})(1-x^{3.0})(1-x^{4.0})(1-x^{6.7})(1-x^{7.5})(1-x^{8.2})}$$ can you please explain me the logic
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### What is the efficient way to calculate number of divisors of N that are divisible by 2?. [closed]

For example if a number is given let say 8 then its factors are 1,2,4,8 hence total numbers of divisors which are divisible by 2 are (2,4,8) that is 3.
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### How to find a certain uppper bound (see details)?

What would be the most efficient way to find this upper bound? Given natural number n and a natural number d < n, find the ...
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### How to derive this formula about the bracket function?

Is there a direct way of proving that $$[nx] = [x] + [x+\frac{1}{2}] + [x+\frac{1}{3}] + \ldots + [x+ \frac{1}{n}]$$ for each real number $x$ and for each positive integer $n$? My effort: Let ...
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### Find a closed expression for a formula including summation

Let: $$\sum\limits_{k = 0}^n {k\left( {\matrix{ n \cr k \cr } } \right)} \cdot {4^{k - 1}} \cdot {3^{n - k}}$$ Find a closed formula (without summation). I think I should define this as a ...
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### Comparing floor and ceiling fractions

Is the following true for all integers x>1: $\lfloor{\frac{2x}{3}}\rfloor \geq \lceil \frac{x}{2}\rceil$
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### Intro to Discrete Math: compound interest calculation

The following is from an intro to discrete mathematics page. It's on compound interest. http://www.cs.odu.edu/~toida/nerzic/content/intro2discrete/intro2discrete.html[1] Scroll to the part with the ...
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### How to scale numbers from one range to another range?

I'm stuck in a problem of mapping numbers from one range to another. I want to calculate popularity of a web page based on the number of page hits on a scale of 10. The problem is total number of web ...
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### Random number x probability in interval [0,10]

So lets say $x=10*rand()$, so x will be equal to a random number on the interval [0,10]. So what is the probability of $2x+1$ rounding to $5$. So one can come up with $4.5<=2x+1<5.5$. Is that ...
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### Chain and sprockets

Consider a sprocket has $s$ teeth, and a chain has $h$ holes. Think about a bicycle chain and the sprocket wheel in the back of the chain. Sprockets are numbered $0 \ldots s-1$ and holes are numbers ...
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### More accurate estimation of mathematical constant $e$

Very often in books and also on Wikipedia we can find that: $$e \approx \left(1+\frac{1}{n}\right)^n$$ but I want more accurate estimation, it means instead using $\approx$ I wonder if I can use ...
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### could not able to understand Project Euler 18. “Maximum path sum I”

According to question, By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. ...
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### $n\le 20$ What is the maximum number of digits representing $n$ with base $4$?
$n\le 20$. What is the maximum number of digits representing $n$ with base $4$? This is a question on a sample test that I'm studying for. My prof hasn't gone over it in class, can someone direct ...
### Help with $7 · 7^{k+2} + 64 · 8^{2k+1}$=$7(7^{k+2} + 8^{2k+1}) + 57 · 8^{2k+1}.$
Could someone please explain why 7 is being subtracted from 64 in: $7 · 7^{k+2} + 64 · 8^{2k+1}$ to make $7(7^{k+2} + 8^{2k+1}) + 57 · 8^{2k+1}.$ Also, how does $7^{k+2}$ get factored by 7 to ...