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$\underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \frac{10^{\sqrt{(\ln...

Prove that: $ $ \underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \frac{10^{\sqrt{(\ln n)^{2} +\ln( n^{2}})}}{n^{2} +1} =+\infty$ $ It is an exercise on first chapters of calculus textbook. I...

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$\underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \left(\sqrt[n]{2}...

Prove that: $ $ \underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \left(\sqrt[n]{2} -1\right)^{n} =0$ $ I would like a solution without integral, limit of real functions or others advanced...

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