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Results tagged with inequalities
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user 37555
for questions involving inequalities, upper and lower bounds.
4
votes
Sum over integer compositions
I assume that $k$ is fixed, while $n$ tends to $\infty$. I claim that for $p=2$ the sum in question is asymptotically equal to $k\zeta(2)^{k-1}n^{-2}$. First consider those partitions, which contain p …
4
votes
Accepted
What is the upper bound for $\int \limits_{2}^{x} \frac{e^{-0.3\sqrt{\ln(t)}}}{\ln^2(t)} dt$?
Write $f(x)=\frac{e^{-0.3\sqrt{\log t}}}{\log^2 t}$. On the interval $[2, xf(x)]$ bound the integral trvially by $xf(x)$. On $[xf(x), x]$ the integrand is close to constant. More precisely, we have
$$ …