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Charlie
  • Member for 10 years, 5 months
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10 votes
3 answers
52k views

Prove that the absolute value of a product is the product of the absolute values of factors.

9 votes
2 answers
12k views

Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$

7 votes
2 answers
823 views

Theorem 3.50 - Principles of Mathematical Analysis - Rudin

7 votes
1 answer
14k views

Continuity of an inverse function.

6 votes
2 answers
1k views

Convergence of the series $\sum\limits_{n=3}^\infty (\log\log n)^{-\log\log n}$

6 votes
3 answers
521 views

Monotonicity of the sequences $\left(1+\frac1n\right)^n$, $\left(1-\frac1n\right)^n$ and $\left(1+\frac1n\right)^{n+1}$

6 votes
0 answers
216 views

Taylor expansion of $x^{1/x}$

5 votes
1 answer
365 views

Test the convergence of the series $\sum \sin [\pi(\sqrt5+2)^n]$ [duplicate]

5 votes
1 answer
318 views

Mathematical Analysis 2nd ed. - Apostol, Exercise 4.2

4 votes
2 answers
122 views

An elementary question about $\varepsilon$.

4 votes
2 answers
111 views

How to show that the limit of this sequence is $L=4$ (ex.8.11 Mathematical Analysis 2nd ed.- Apostol)

4 votes
3 answers
182 views

sequence defined by $u_0=1/2$ and the recurrence relation $u_{n+1}=1-u_n^2$

4 votes
1 answer
2k views

Test for convergence of $\sum_{n=2}^\infty(\ln n)^p$

4 votes
1 answer
3k views

Convergence Test $\sum_{n=2}^\infty\frac{1}{n^p-n^q}$

4 votes
1 answer
778 views

Method of Moments - What's the logic?

4 votes
2 answers
110 views

Test the convergence of the series $\sum\limits_nn^p(\sqrt{n+1}-2\sqrt n + \sqrt{n-1})$

3 votes
2 answers
119 views

Strategy for tackling the $\lim_{n\to+\infty}\frac{(-1)^nn}{(1+n)^n}$

2 votes
1 answer
3k views

Theorem 9.5 Cauchy Condition for uniform convergence of series - Math Analysis 2nd ed - Apostol

2 votes
3 answers
2k views

Theorem 9.7 - Uniform convergence and continuity of the limit function - Math Analysis 2nd ed - Apostol

2 votes
2 answers
260 views

Theorem 8.19 - Mathematical Analysis 2nd ed. - Apostol

2 votes
1 answer
216 views

Proof of Theorem 8.25 (Ratio Test for a series) - Mathematical Analysis 2nd ed. - Apostol

2 votes
3 answers
141 views

Proof of $\lim \limits_{n\to\infty}\left(\frac{a_n+b_n}{2}\right)^n=\sqrt{ab}$

2 votes
5 answers
364 views

Prove that the series$\sum a_n$, with $a_n$ defined recursively, converges to 1

2 votes
1 answer
56 views

Find the limit of $\frac{1}{n^2}\sum_{k=1}^n k^2\sin\left(\frac{\theta}{k}\right)$

2 votes
1 answer
334 views

Uniform integrability of a sequence of functions.

2 votes
2 answers
106 views

Proving the convergence of $a_{n+2}=(a_{n+1}a_n)^{1/2} \qquad (a_1\ge0, a_2\ge0)$

2 votes
1 answer
717 views

Check that an Ito integral is a martingale.

1 vote
1 answer
135 views

Static game of incomplete information.

1 vote
3 answers
85 views

Is $(n^{1/n}-1)\in O(n^{-\frac12})$ as $n\to \infty$?

1 vote
1 answer
154 views

Convergence of $\sum\limits_{n=2}^\infty n^p\left(\frac{1}{\sqrt{n-1}}-\frac{1}{\sqrt n}\right)$