7
$\begingroup$

How can I show that$$\sqrt[3]6>\int_1^\infty\frac{(1+x)^{1/3}}{x^2}\mathrm dx?$$

  • 0
    Perhaps you can try to use a Taylor expansion on $(1+x)^{1/3}$ and use a suitable convergence theorem (e.g. Monotone convergence theorem, Fatou's lemma or the Dominated convergence theorem)2012-08-03

5 Answers 5