# Tagged Questions

37 views

### Approximating 'big' ratio with 'small' ratio

Given a ratio $\frac{m}{n}, p \in N, q \in N$ where either $m$ or $n$ (or both) is a very big number, how can we find a ratio $\frac{p}{q}, p \in N, q \in N$ which estimates $\frac{m}{n}$ up to ...
72 views

### Factoring/approximating an apparently simple formula

Does anyone know if the following formula can be factorized or approximated: $a^3 + b^3 + c^3 + a^2b + ab^2 + a^2c + ac^2 + b^2c + bc^2 + abc$ It looks a lot like $(a + b + c)^3$, except for the ...
95 views

### Aproximate calculation in decimals

I am trying to refresh on precision of calculations. If we have the decimal fractions: $.234673$, $.322135$, $.114342$, $.563217$ each known to be correct to six figures why are each of the decimals ...
Stirling approximation to a factorial is $$n! \sim \sqrt{2 \pi n} \left(\frac{n}{e}\right)^n.$$ I wonder what benefit can be got from it? From computational perspective (I admit I don't ...
I can calculate the result of $x^y$ provided that $y \in\mathbb{N}, x \neq 0$ using a simple recursive function:  f(x,y) = \begin {cases} 1 & y = 0 \\ (x)f(x, y-1) & y > 0 \end ...