Newbetuts

Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$ [duplicate]

The domino curve

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$

Without superior math, can we evaluate this limit?

How find limit $\displaystyle \lim_{n\to\infty}n\left(1-\tfrac{\ln n}{n}\right)^n$

Derivative of exponential function proof

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

how to evaluate $\lim_{x\to0} (x^2)/(e^x-1) $ without L'Hospital

Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$

Limit of maximum of $f_{n}(x)=\frac{1}{n}(\sin{x}+\sin{(2x)}+\cdots+\sin{(nx)})$

Calculating a limit using dominated convergence theorem

How come $\lim_{x\to0}$ $x^x = 1$?

What is $ \lim_{n\to\infty}\frac{1}{e^n}\Bigl(1+\frac1n\Bigr)^{n^2}$?

A limit involving the Thue–Morse sequence

New posts in limits

Limit involving $(\sin x) /x -\cos x $ and $(e^{2x}-1)/(2x)$, without l'Hôpital

Limits of functions that can't be attacked by Taylor series or L'hopital's rule

Prove that when x approaches to 1, function 1/(x-1) doesn't have limit

$\lim_{n\rightarrow \infty}(1+\frac{r}{n})^n$ is equal to ${e^{r}}$?

Does $\lim_{x\to0}\frac{xf'(x)}{f(x)}$ exist when $f(0)=0$, $f'(0)=0$?

Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$ [duplicate]

The domino curve

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$

Without superior math, can we evaluate this limit?

How find limit $\displaystyle \lim_{n\to\infty}n\left(1-\tfrac{\ln n}{n}\right)^n$

Derivative of exponential function proof

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

how to evaluate $\lim_{x\to0} (x^2)/(e^x-1) $ without L'Hospital

Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$

Limit of maximum of $f_{n}(x)=\frac{1}{n}(\sin{x}+\sin{(2x)}+\cdots+\sin{(nx)})$

Calculating a limit using dominated convergence theorem

How come $\lim_{x\to0}$ $x^x = 1$?

What is $ \lim_{n\to\infty}\frac{1}{e^n}\Bigl(1+\frac1n\Bigr)^{n^2}$?

A limit involving the Thue–Morse sequence