Question

limitof the series $\sum_{k=2}^{\infty}{\frac{2^{k+1}+3^k}{4^{k-1}}}$

score 74 · Answer 1 · 2026-04-09 21:15:45

74

Views

limitof the series $\sum_{k=2}^{\infty}{\frac{2^{k+1}+3^k}{4^{k-1}}}$

Published on 09 Apr 2026 - 21:15

score 124 · Answer 2 · 2026-04-15 06:18:57

124

Views

if the projection of $E\subseteq \mathbb{R}^n$ onto $\mathbb{R}^{n-1}$ has (n-1) dim. measure zero, then the set $E$ has $n$-dim. measure zero

Published on 15 Apr 2026 - 6:18

score 49 · Answer 3 · 2026-04-10 19:56:51

49

Views

Does the function have a factor as a power of 2?

Published on 10 Apr 2026 - 19:56

score 127 · Answer 4 · 2026-04-16 18:57:35

127

Views

Radius of convergence of $\sum_{n=1}^\infty n!\left(\frac{z^n}{n}\right)^n$

Published on 16 Apr 2026 - 18:57

score 228 · Answer 5 · 2026-04-15 14:45:24

228

Views

Proving that a map between a normed space and its dual is well defined

Published on 15 Apr 2026 - 14:45

score 44 · Answer 6 · 2026-04-16 20:42:04

44

Views

$cl_f(A)=\bigcup_{n \in \mathbb{N}}A_n$

Published on 16 Apr 2026 - 20:42

score 1.3k · Answer 7 · 2026-03-27 08:16:30

1.3k

Views

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Published on 27 Mar 2026 - 8:16

score 184 · Answer 8 · 2026-04-14 07:43:53

184

Views

The notion of a smooth function on a manifold in Guillemin and Pollack

Published on 14 Apr 2026 - 7:43

score 1.1k · Answer 9 · 2026-04-13 13:15:23

1.1k

Views

proof of continuity of coordinate functions (Rudin)

Published on 13 Apr 2026 - 13:15

score 110 · Answer 10 · 2026-04-13 17:47:19

110

Views

how can I calculate: $\lim_{n \to \infty} \frac{\frac{1}{n}-\ln(1+\frac{1}{n})}{n^{\frac{1}{n}}-1} $?

Published on 13 Apr 2026 - 17:47

score 104 · Answer 11 · 2026-04-16 13:42:11

Does there exist a continuous function $f :\mathbb{R} \rightarrow \mathbb{R}$ such that $f \circ f(x) = -x$ for all $x$?

score 143 · Answer 12 · 2026-04-13 17:24:06

143

Views

Is it known how to evaluate $\int_0^1\frac{(1-x)x^{n+1}}{\sin (\pi x)}dx$, for integers $n\geq 1$?

Published on 13 Apr 2026 - 17:24

score 363 · Answer 13 · 2026-04-15 15:34:27

363

Views

How to solve $\int \sin^3(x) \cos^2(x) dx$ with integration by parts?

Published on 15 Apr 2026 - 15:34

score 50 · Answer 14 · 2026-04-18 18:24:40

50

Views

If $f$ is monotonic and its limits at $\pm\infty$ are equal, then $f$ is constant?

Published on 18 Apr 2026 - 18:24

score 53 · Answer 15 · 2026-04-20 06:04:41

53

Views

Find a continuous function, over the unit interval, satisfying $\int_0^x f(u)du\geq \sum_{n=1}^\infty\frac{\mu(n)}{n^2}x^{n-1}$ for each $ x\in[0,1]$

Published on 20 Apr 2026 - 6:04

List Question

limitof the series $\sum_{k=2}^{\infty}{\frac{2^{k+1}+3^k}{4^{k-1}}}$

if the projection of $E\subseteq \mathbb{R}^n$ onto $\mathbb{R}^{n-1}$ has (n-1) dim. measure zero, then the set $E$ has $n$-dim. measure zero

Does the function have a factor as a power of 2?

Radius of convergence of $\sum_{n=1}^\infty n!\left(\frac{z^n}{n}\right)^n$

Proving that a map between a normed space and its dual is well defined

$cl_f(A)=\bigcup_{n \in \mathbb{N}}A_n$

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

The notion of a smooth function on a manifold in Guillemin and Pollack

proof of continuity of coordinate functions (Rudin)

how can I calculate: $\lim_{n \to \infty} \frac{\frac{1}{n}-\ln(1+\frac{1}{n})}{n^{\frac{1}{n}}-1} $?

Does there exist a continuous function $f :\mathbb{R} \rightarrow \mathbb{R}$ such that $f \circ f(x) = -x$ for all $x$?

Is it known how to evaluate $\int_0^1\frac{(1-x)x^{n+1}}{\sin (\pi x)}dx$, for integers $n\geq 1$?

How to solve $\int \sin^3(x) \cos^2(x) dx$ with integration by parts?

If $f$ is monotonic and its limits at $\pm\infty$ are equal, then $f$ is constant?

Find a continuous function, over the unit interval, satisfying $\int_0^x f(u)du\geq \sum_{n=1}^\infty\frac{\mu(n)}{n^2}x^{n-1}$ for each $ x\in[0,1]$

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