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roman
  • Member for 9 years, 8 months
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10 votes
Accepted

Proof that $\lim_{n \to \infty} n[\log (n+1)-\log(n)]=1$

8 votes

An example of a sequence which does not have any subsequence with a finite limit.

6 votes

Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$

4 votes
Accepted

Solving $\lim_{x\to+\infty}{x^2(\cos(\frac{\pi}{x+2})-1)}$

4 votes
Accepted

Evaluate the limit of the sequence: $\lim_{n_\to\infty}\frac{\sqrt{(n-1)!}}{(1+\sqrt{1})\cdot(1+\sqrt{2})\cdot (1+\sqrt{3})\cdots (1+\sqrt{n})}$

4 votes

Prove that $\lim_{n\to\infty} (\sqrt{n^2+n}-n) = \frac{1}{2}$

3 votes

Find $\lim_{x \to 0} (\sin x)^{1/x} + (1/x)^{\sin x}$

3 votes
Accepted

How to prove $\lim_{n\to\infty}\frac{1}{\sqrt[n]{n!}}=0 $

3 votes

Determining the minimum value of the function $y = x + 2\sqrt{x^2 - \sqrt{2}x + 1}$

3 votes

Solving integral $\int \frac{\ln x-1}{\ln^2x}dx$

2 votes

How do I prove the identities of these questions?

2 votes

Monotonicity of $a_n=1+\frac{(-1)^n}{n}$

2 votes

Riemman sum of $1/x^3$

2 votes

Help understanding the steps of a solved limit

1 vote

Trouble solving recursive function

1 vote

Compute $ \lim\limits_{n \to \infty}\frac{\sqrt{3n^2+n-1}}{n+\sqrt{n^2-1}}$

1 vote
Accepted

How to solve $\lim \left(\frac{n^3+n+4}{n^3+2n^2}\right)^{n^2}$

1 vote

Why does $\lim\limits_{x\rightarrow0}\frac{1}{2x-1} \log(2^{1+\sin{x}}-1) = 2 $?

1 vote

Error evaluating $ \lim_{x\to 0}\frac{x-\tan x}{x^3} $

1 vote

A sequence $\{a_n\}$ is such that $\lim_n(a_{n+1} - a_n) = 0$. Given some additional properties of $a_n$ prove that it converges.

1 vote

Different methods of evaluating $\int\sqrt{a^2-x^2}dx$:

1 vote

Proof verification that $\{x_n\} = 0,\underbrace{77\dots 7}_{\text{n times}}$ is a Cauchy sequence.

1 vote

Recursive proof that $n^n \geq n!$

1 vote

Prove that $C_{3 \over 2}^n$ is bounded given $C_{a}^n = \frac{a(a-1)(a-2)\dots(a-n+1)}{n!}$

1 vote

Riemann sum of $\int_1^2 {1\over x^2} dx$.

0 votes

Prove that $\lim_{n \to\infty}(1+\frac{1}{n})^n =\lim_{n \to\infty} (\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots + \frac{1}{n!})$

0 votes

Show that if $\{x_n\}$ converge and $\{y_n\}$ diverge then $\{ax_n + by_n\}$ diverge, for $b \ne 0$

0 votes

For $f(x) = ax^2 -2 + {1\over x}$, find the smallest $a$ such that $\{\forall x \gt 0: f(x) \ge 0\}$

0 votes
Accepted

How do I compute $\lim_{x \to a}(a-x)\tan\left(\frac{πx}{2a}\right)$

0 votes

Prove any number $c \in [a, b]$ is a subsequential limit if $\lim\inf x_n = a$, $\lim \sup x_n = b$, $a\ne b$, $\lim(x_n -x_{n+1})=0$