As [math]x\to\infty\displaystyle\lim_{x=1}\frac{d_{x}}{\left(x+1\right)^{2}}=1[/math] how can we prove [math]\left[a_{x}<b_{x}<c_{x}<d_{x}\right]\in X_{x}\mapsto X_{x+1}[/math] and [math]\left(d_{x}-1\right)-\left(a_{x}-1\right)=3x [/math]?
insincere question