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16 Questions

views newest activity votes

9

votes

2

answers

136

views

Sum of a rearranged alternating harmonic series, with three positive terms followed by one negative term

real-analysis sequences-and-series analysis

nov 2 '11 at 5:29 robjohn♦ 59.7k

1

5

votes

1

answer

518

views

Using the Taylor expansion for ${(1+x)}^{-1/2}$, evaluate $\sum_{n=0}^\infty \binom{2n}{n} a^n$

homework real-analysis binomial-coefficients taylor-expansion

nov 15 '11 at 21:22 dhz 194

4

votes

3

answers

229

views

If the closures of two subsets of a topological space are equal, are the closures of the images of the two subsets under a continuous map also equal?

general-topology

may 16 '12 at 16:28 wildildildlife 2,850

3

votes

1

answer

80

views

Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?

measure-theory integration

jun 6 '12 at 23:40 Norbert 20.3k

2

votes

1

answer

74

views

Show that the series representation of the Bessel function works

homework sequences-and-series differential-equations special-functions power-series

nov 26 at 9:58 joriki 92.6k

2

votes

2

answers

178

views

What is $\limsup\limits_{n\to\infty} \cos (n)$, when $n$ is a natural number?

real-analysis analysis

apr 25 '12 at 18:20 Thomas Andrews 29.8k

2

votes

1

answer

243

views

Is it possible that in a metric space $(X, d)$ with more than one point, the only open sets are $X$ and $\emptyset$?

real-analysis general-topology metric-spaces

dec 1 '11 at 3:07 Srivatsan 15.6k

1

vote

1

answer

52

views

Suppose that $f(z)$ is meromorphic on a disk, show that negative powers in the Laurent series of $f(z)$ is the sum of the principal parts of its poles

homework sequences-and-series complex-analysis

dec 7 at 16:35 wisefool 988

1

vote

1

answer

38

views

If $(a_n)_n$ is bounded, then $\sum\limits_n a_{n}n^{-z}$ converges uniformly for $\Re z \geq 1+\epsilon$

homework complex-analysis complex-numbers

nov 8 at 7:40 Did 103k

1

vote

0

answers

101

views

Prove that if $A$ is null and $f: \mathbb{R} \longrightarrow \mathbb{R}$ has a continuous derivative, then $f(A)$ is null

homework real-analysis analysis measure-theory contour-integration

apr 26 '12 at 1:46 Henry T. Horton 7,524

1

1

vote

1

answer

157

views

Why is this relation an equivalence relation on $G\setminus \{e\}$ if and only if $o(g)$ is prime for each $g \in G\setminus \{e\}$?

homework abstract-algebra group-theory

jan 26 '12 at 3:33 Arturo Magidin 158k

1

vote

1

answer

310

views

$X, Y \subset \mathbb{R}^n$. Define $d(K, F) = \inf\{ d(x,y), x \in K, y \in F\}$, show that $d(a,b) = d(K,F)$ for some $a$, $b$

homework general-topology analysis metric-spaces

dec 2 '11 at 16:45 t.b. 43.2k

1

vote

1

answer

72

views

Is the function $\sum_{n=0}^{\infty} \frac{n^2x}{1+n^4x^2}$ continuous in $x \in (0, 1]$?

homework real-analysis sequences-and-series analysis

nov 30 '11 at 1:14 Robert Israel 86.4k

0

votes

2

answers

231

views

Show that $\sum \frac{z^k}{k}$ does not converge uniformly for |z|<1

homework complex-analysis complex-numbers

nov 8 at 14:03 robjohn♦ 59.7k

0

votes

2

answers

150

views

Proof that a semidirect product with trivial action is the direct product

homework abstract-algebra group-theory

feb 8 '12 at 17:04 Community♦ 1

0

votes

1

answer

50

views

Showing that $X_0=X$, $X_1=f(X_0)$, $X_2=f(X_1)$, etc. are nested

homework general-topology analysis

dec 2 '11 at 6:08 Brian M. Scott 154k

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