Question

Examining whether $\sum \limits_{n=0}^\infty\frac{(-1)^{n+1}}{5n+1}$ is convergent, absolute convergent or divergent

score 137 · Answer 1 · 2026-03-31 11:32:53

137

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Examining whether $\sum \limits_{n=0}^\infty\frac{(-1)^{n+1}}{5n+1}$ is convergent, absolute convergent or divergent

Published on 31 Mar 2026 - 11:32

score 80 · Answer 2 · 2026-04-16 01:34:58

80

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Laurent Series for $f(z)=\frac{2}{(z+1)^2}-\frac{5}{z-5}$

Published on 16 Apr 2026 - 1:34

score 121 · Answer 3 · 2026-04-16 14:49:54

121

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Where is $k(z)=PV(z-1)^{\frac{1}{2}}PV(z+1)^{\frac{1}{2}}$ Continuous and Differentiable

Published on 16 Apr 2026 - 14:49

score 166 · Answer 4 · 2026-04-13 20:07:40

166

Views

Prove that if $u\in \mathbb{Z}[\sqrt{2}]$ (Euclidean domain) is unit, then $v(u)=1$.

Published on 13 Apr 2026 - 20:07

score 120 · Answer 5 · 2026-04-09 18:09:13

120

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Showing that set the of algebraic numbers are countable [Proof verification]

Published on 09 Apr 2026 - 18:09

score 261 · Answer 6 · 2026-04-16 03:10:38

261

Views

Show that $\int_0^{\pi} \dfrac{\cos2\theta \ d \theta}{1-2 a \cos {\theta} +a^2}=\dfrac{a^2 \pi}{1-a^2}; \ \ (-1<a<1). $

Published on 16 Apr 2026 - 3:10

score 1.5k · Answer 7 · 2026-04-15 11:21:47

1.5k

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Find poles of $f(z)=\frac{z}{(z-1)(z-2)^2}$ , calculate residues at the poles and then evaluate $\int_C f(z)dz$ where $C:|z+1-i|=2$

Published on 15 Apr 2026 - 11:21

score 597 · Answer 8 · 2026-04-16 18:12:43

597

Views

There are infinitely many primes $p \equiv 7 (\text{mod} \ 8).$

Published on 16 Apr 2026 - 18:12

score 130 · Answer 9 · 2026-04-12 05:31:49

130

Views

Find the density of random variable $Z=X/Y$

Published on 12 Apr 2026 - 5:31

score 146 · Answer 10 · 2026-03-25 11:54:21

146

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Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$?

Published on 25 Mar 2026 - 11:54

score 32 · Answer 11 · 2026-04-12 14:14:52

32

Views

[Proof-Verification]Homeorphism between open unit ball, unit hypercube and $\mathbb R^n$

Published on 12 Apr 2026 - 14:14

score 69 · Answer 12 · 2026-04-13 00:13:37

69

Views

Partial derivative under integral sign

Published on 13 Apr 2026 - 0:13

score 92 · Answer 13 · 2026-04-16 09:54:36

92

Views

Proof verification of $\sum_{k=1}^n kq^{n-k}$ is unbounded for $n \in \mathbb N$ and $q\in\{\mathbb R\setminus0\}$

Published on 16 Apr 2026 - 9:54

score 113 · Answer 14 · 2026-04-17 11:56:51

113

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$\epsilon-\delta$ proof for $ \lim _ {x \rightarrow 9}\frac{x-9}{\sqrt{x}-3}=6. $

Published on 17 Apr 2026 - 11:56

score 108 · Answer 15 · 2026-04-15 06:47:00

108

Views

Derivation of Ordinary Least-Squares Slope Estimate

Published on 15 Apr 2026 - 6:47

List Question

Examining whether $\sum \limits_{n=0}^\infty\frac{(-1)^{n+1}}{5n+1}$ is convergent, absolute convergent or divergent

Laurent Series for $f(z)=\frac{2}{(z+1)^2}-\frac{5}{z-5}$

Where is $k(z)=PV(z-1)^{\frac{1}{2}}PV(z+1)^{\frac{1}{2}}$ Continuous and Differentiable

Prove that if $u\in \mathbb{Z}[\sqrt{2}]$ (Euclidean domain) is unit, then $v(u)=1$.

Showing that set the of algebraic numbers are countable [Proof verification]

Show that $\int_0^{\pi} \dfrac{\cos2\theta \ d \theta}{1-2 a \cos {\theta} +a^2}=\dfrac{a^2 \pi}{1-a^2}; \ \ (-1<a<1). $

Find poles of $f(z)=\frac{z}{(z-1)(z-2)^2}$ , calculate residues at the poles and then evaluate $\int_C f(z)dz$ where $C:|z+1-i|=2$

There are infinitely many primes $p \equiv 7 (\text{mod} \ 8).$

Find the density of random variable $Z=X/Y$

Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$?

[Proof-Verification]Homeorphism between open unit ball, unit hypercube and $\mathbb R^n$

Partial derivative under integral sign

Proof verification of $\sum_{k=1}^n kq^{n-k}$ is unbounded for $n \in \mathbb N$ and $q\in\{\mathbb R\setminus0\}$

$\epsilon-\delta$ proof for $ \lim _ {x \rightarrow 9}\frac{x-9}{\sqrt{x}-3}=6. $

Derivation of Ordinary Least-Squares Slope Estimate

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