# Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

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### What would be a good metric that puts heavier weight on a longer time period?

I'm currently trying to think of a metric to measure a performance of a product that gives higher points to longer contracts. For example, let's say that one contract A is a year long contract and the ...
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Let P be a real number such that $1<P<2$, and $m,n\in\mathbb{N}$ where $m<n$. Let $y\in\mathbb{N}$, and suppose that $y>1+\frac{1}{\sqrt[n-m]{2/P}-1}$. I am trying to show that $\left(\... 2 votes 1 answer 62 views ### How consistent can solving an equation be if one way of solving it might give an undefined answer? If solving for an equation one way gives me an undefined answer, does that mean solving it in other ways too will give me an undefined answer? If no, then how consistent is math? (I'm not sure if I'm ... -1 votes 1 answer 35 views ### On inequality of fractions and exponential expressions [closed] I am having a hard time proving this proposition: Show that for$x_i, n \in \mathbb{N}$, where$x_i\geq 2$and for any real number$r>1$, if$\prod\limits_{i=1}^{n}\left(1-\frac{1}{x_i}\right) \leq ...
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I am reading a mathematical paper and they use this concave looking equals sign: I was unable to find how to write this in LaTeX. I don't even know what this sign is called. They use it to denote ...
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### Sum of $\frac{25^x}{25^x+5}$

Find $$\sum_{n=1}^{1999}\frac{25^{\frac{n}{2000}}}{25^{\frac{n}{2000}}+5}$$ My work: $$\frac{25^x}{25^x+5}=\frac{5^{2x}}{5^{2x}+5 }$$ I don't see a pattern here, and I don't think the point of this ...
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