Question

Intersection of maximal ideals of $\mathbb{Q}[x]/(f(x))$ are nilpotent elements

score 224 · Answer 1 · 2026-04-17 14:15:45

224

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Intersection of maximal ideals of $\mathbb{Q}[x]/(f(x))$ are nilpotent elements

Published on 17 Apr 2026 - 14:15

score 279 · Answer 2 · 2026-04-14 19:13:19

279

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Show that if $|z| < 1$ then the series $\sum_{n=0}^{\infty}(n+1)z^{n}$ converges, and find its sum.

Published on 14 Apr 2026 - 19:13

score 75 · Answer 3 · 2026-04-15 23:04:51

75

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Show that if $\sum_{n=1}^{\infty}a_{n}$ converges, then so do $\sum_{n=1}^{\infty}a^{2}_{n}$ and $\sum_{n=1}^{\infty}a_{n}/(1-a_{n})$.

Published on 15 Apr 2026 - 23:04

score 92 · Answer 4 · 2026-04-15 12:09:54

92

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If matrix $X$ & $Y$ anti-commute then show that the two matrices are linearly independent

Published on 15 Apr 2026 - 12:09

score 120 · Answer 5 · 2026-04-10 14:15:51

120

Views

What will be the sum of some 3 consecutive numbers must be at least?

Published on 10 Apr 2026 - 14:15

score 71 · Answer 6 · 2026-04-16 11:13:54

71

Views

Proving that $\rho_E(x) = \inf_{z \in E} d(x, z) = 0$ iff $x \in \bar E$ (Baby Rudin Exercise 20 Chapter 4)

Published on 16 Apr 2026 - 11:13

score 83 · Answer 7 · 2026-04-17 01:22:16

83

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Prove that $L(f,P)=\inf\{\sum_{R\in P} f(x_R)\cdot v(R):x_R\in R\}$ and $U(f,P)=\sup\{\sum_{R\in P} f(x_R)\cdot v(R):x_R\in R\}$

Published on 17 Apr 2026 - 1:22

score 1k · Answer 8 · 2026-04-16 05:41:01

1k

Views

Prove that $\sqrt{x} > \ln x$ for all $x>0$ with a study of function

Published on 16 Apr 2026 - 5:41

score 107 · Answer 9 · 2026-04-11 16:04:13

107

Views

Paradox of Fake Choice

Published on 11 Apr 2026 - 16:04

score 113 · Answer 10 · 2026-04-09 04:14:35

113

Views

About the smallest value of B

Published on 09 Apr 2026 - 4:14

score 121 · Answer 11 · 2026-04-11 19:13:35

121

Views

Prove that multiplication of residue classes in $\mathbb{Z}/n\mathbb{Z}$ is associative.

Published on 11 Apr 2026 - 19:13

score 45 · Answer 12 · 2026-04-09 11:25:28

45

Views

Finding number of solutions?

Published on 09 Apr 2026 - 11:25

score 88 · Answer 13 · 2026-04-14 10:24:35

88

Views

Determine the number of ordered triples

Published on 14 Apr 2026 - 10:24

score 312 · Answer 14 · 2026-04-16 20:37:04

312

Views

Any multiplicative subgroup of a finite field is cyclic

Published on 16 Apr 2026 - 20:37

score 138 · Answer 15 · 2026-04-12 09:51:28

138

Views

Problematic solution related to finding the function range

Published on 12 Apr 2026 - 9:51

List Question

Intersection of maximal ideals of $\mathbb{Q}[x]/(f(x))$ are nilpotent elements

Show that if $|z| < 1$ then the series $\sum_{n=0}^{\infty}(n+1)z^{n}$ converges, and find its sum.

Show that if $\sum_{n=1}^{\infty}a_{n}$ converges, then so do $\sum_{n=1}^{\infty}a^{2}_{n}$ and $\sum_{n=1}^{\infty}a_{n}/(1-a_{n})$.

If matrix $X$ & $Y$ anti-commute then show that the two matrices are linearly independent

What will be the sum of some 3 consecutive numbers must be at least?

Proving that $\rho_E(x) = \inf_{z \in E} d(x, z) = 0$ iff $x \in \bar E$ (Baby Rudin Exercise 20 Chapter 4)

Prove that $L(f,P)=\inf\{\sum_{R\in P} f(x_R)\cdot v(R):x_R\in R\}$ and $U(f,P)=\sup\{\sum_{R\in P} f(x_R)\cdot v(R):x_R\in R\}$

Prove that $\sqrt{x} > \ln x$ for all $x>0$ with a study of function

Paradox of Fake Choice

About the smallest value of B

Prove that multiplication of residue classes in $\mathbb{Z}/n\mathbb{Z}$ is associative.

Finding number of solutions?

Determine the number of ordered triples

Any multiplicative subgroup of a finite field is cyclic

Problematic solution related to finding the function range

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