### Questions (6)

 3 Find $\lim_{n \to \infty}(n - \frac{1}{2^n} \sum_{k=1}^{2^n}\log_{2}(k+2^{n-1}))$ using Riemann sums 3 How to show that $\lim_{n\to \infty } \left(\frac{(1 + \frac{1}{n^2})^{n^2}}{e}\right)^n = 1$? 2 How to prove $\{n!e\} = \frac{1}{n +1} + \frac{1}{(n+1)(n+2)} + \frac{1}{(n+1)(n+2)(n+3)} + \dots$ 0 I need to show that functional series $\sum_{n=1}^{+\infty}\frac{\sqrt{n+x^2}}{n^2+e^x}$ is differentiable 0 Show that $\lim_{n \to +\infty} \sqrt[n]{e^n - (\sqrt{e})^n} = e$

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### Tags (12)

 0 calculus × 6 0 summation 0 sequences-and-series × 3 0 uniform-convergence 0 limits × 2 0 derivatives 0 riemann-sum 0 factorial 0 sequence-of-function 0 fractions

### Bookmarks (3)

 8 Show the series $\sum (2^{1/n}-1)$ diverges 2 Find if this sequence has a limit 1 Show uniform convergence of a series involving ln function

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 Mathematics 99 rep 44 bronze badges Stack Overflow 11 rep 22 bronze badges