Question

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

score 281 · Answer 1 · 2026-04-16 20:56:01

281

Views

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Published on 16 Apr 2026 - 20:56

score 44 · Answer 2 · 2026-04-09 13:38:17

Relationship of the roots of two polynomials both which have the same constant and x term but vary in the x^3 term by a function of the x coefficient

score 91 · Answer 3 · 2026-04-12 20:13:21

91

Views

Is there a field $k$ in which $x^3+3$ has double roots?

Published on 12 Apr 2026 - 20:13

score 107 · Answer 4 · 2026-04-16 05:34:08

107

Views

Prove that $a_n\ge 1$ for all $n\ge 1$ with equality iff $n=1,2,4,5$

Published on 16 Apr 2026 - 5:34

score 134 · Answer 5 · 2026-04-12 07:09:46

134

Views

Rolle's Theorem in proving exactly one real zero

Published on 12 Apr 2026 - 7:09

score 167 · Answer 6 · 2026-04-12 12:44:22

167

Views

Bisection Method : Estimating Iterations needed to approximate a root within three decimal places

Published on 12 Apr 2026 - 12:44

score 94 · Answer 7 · 2026-04-14 22:35:18

94

Views

Zeros of $f(z) = \sum_{n= 0}^{\infty} \frac{z^n}{n!\exp(\ln^2(n+1))} $ and $\lim_{x \to -\infty} f(x) = A $?

Published on 14 Apr 2026 - 22:35

score 78 · Answer 8 · 2026-04-09 12:26:38

78

Views

Finding root of nonlinear equation in interval

Published on 09 Apr 2026 - 12:26

score 31 · Answer 9 · 2026-03-26 08:03:21

31

Views

Reference for Zassenhaus bound of roots of polynomial

Published on 26 Mar 2026 - 8:03

score 122 · Answer 10 · 2026-04-17 01:49:29

122

Views

Why for a real number $x$ and an even integer $n, x^{1/n}$ is not real if $x<0$?

Published on 17 Apr 2026 - 1:49

score 229 · Answer 11 · 2026-04-14 15:44:32

229

Views

When is the square root differentiable?

Published on 14 Apr 2026 - 15:44

score 47 · Answer 12 · 2026-04-13 14:46:30

47

Views

Find the equation whose roots are twice the negative reciprocal of the roots

Published on 13 Apr 2026 - 14:46

score 57 · Answer 13 · 2026-04-13 02:41:59

57

Views

Root of a negative real number - mistake in GRE Question?

Published on 13 Apr 2026 - 2:41

score 39 · Answer 14 · 2026-04-12 00:31:12

39

Views

Understanding Gradient descent with momentum equations

Published on 12 Apr 2026 - 0:31

score 89 · Answer 15 · 2026-04-14 16:02:00

89

Views

Do simple roots on most slices imply a polynomial is square free?

Published on 14 Apr 2026 - 16:02

List Question

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Relationship of the roots of two polynomials both which have the same constant and x term but vary in the x^3 term by a function of the x coefficient

Is there a field $k$ in which $x^3+3$ has double roots?

Prove that $a_n\ge 1$ for all $n\ge 1$ with equality iff $n=1,2,4,5$

Rolle's Theorem in proving exactly one real zero

Bisection Method : Estimating Iterations needed to approximate a root within three decimal places

Zeros of $f(z) = \sum_{n= 0}^{\infty} \frac{z^n}{n!\exp(\ln^2(n+1))} $ and $\lim_{x \to -\infty} f(x) = A $?

Finding root of nonlinear equation in interval

Reference for Zassenhaus bound of roots of polynomial

Why for a real number $x$ and an even integer $n, x^{1/n}$ is not real if $x<0$?

When is the square root differentiable?

Find the equation whose roots are twice the negative reciprocal of the roots

Root of a negative real number - mistake in GRE Question?

Understanding Gradient descent with momentum equations

Do simple roots on most slices imply a polynomial is square free?

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