Question

If $a_n > 0$ and $\lim_{n \to \infty}{\sqrt{a_n}}>1$ show that $\lim_{n \to \infty}a_n$ exists.

score 155 · Answer 1 · 2026-04-24 11:15:12

155

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If $a_n > 0$ and $\lim_{n \to \infty}{\sqrt{a_n}}>1$ show that $\lim_{n \to \infty}a_n$ exists.

Published on 24 Apr 2026 - 11:15

score 244 · Answer 2 · 2026-05-10 17:15:07

244

Views

Calculus problem regarding graph of derivative of a function

Published on 10 May 2026 - 17:15

score 608 · Answer 3 · 2026-04-14 02:02:41

608

Views

How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below?

Published on 14 Apr 2026 - 2:02

score 928 · Answer 4 · 2026-04-16 20:54:53

928

Views

Proving that euclidean distance is uniform continuous by the two variables

Published on 16 Apr 2026 - 20:54

score 337 · Answer 5 · 2026-04-15 19:27:43

337

Views

How can I prove the Wolfram Alpha result $\int_0^{\infty} \frac{(\sin x)^2}{x^2-\pi ^2} dx=-\frac1{2\pi}$?

Published on 15 Apr 2026 - 19:27

score 63 · Answer 6 · 2026-05-10 13:51:29

63

Views

how to show that $\Delta [\frac{c- |x-a|^2}{|x-b|^n}] = 2n|x-b|^{-n-2}(c-|a-b|^2), \; x \neq b$

Published on 10 May 2026 - 13:51

score 1k · Answer 7 · 2026-04-15 07:14:06

1k

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What is the closest point to $(0,-1/2)$ on the curve $x^2+2y=0$? Why can't I differentiate over $y$?

Published on 15 Apr 2026 - 7:14

score 85 · Answer 8 · 2026-05-14 16:06:41

85

Views

Roots of a Quadratic Equation - Upper Bounding

Published on 14 May 2026 - 16:06

score 128 · Answer 9 · 2026-05-14 13:52:23

128

Views

what does $f''$ suggests about the graph of $f$?

Published on 14 May 2026 - 13:52

score 149 · Answer 10 · 2026-04-16 02:17:31

149

Views

Showing $\;\ln(\ln(1+\frac{1}{\vert x \vert}))\notin L^{\infty}(\{\vert x \vert \lt 1\})\;$

Published on 16 Apr 2026 - 2:17

score 69 · Answer 11 · 2026-04-11 18:21:51

69

Views

guessing the value based on derivative

Published on 11 Apr 2026 - 18:21

score 233 · Answer 12 · 2026-05-10 15:45:26

233

Views

Surface integral of spherical shell in a $e^{-x^2}$ field

Published on 10 May 2026 - 15:45

score 143 · Answer 13 · 2026-04-12 08:35:48

143

Views

Proof verification: derivative of $x^n$

Published on 12 Apr 2026 - 8:35

score 36 · Answer 14 · 2026-04-24 11:09:18

36

Views

Horizontal asymptotes of function defined as an inequation

Published on 24 Apr 2026 - 11:09

score 49 · Answer 15 · 2026-04-08 18:26:23

49

Views

When is equation has a unique solution?

Published on 08 Apr 2026 - 18:26

List Question

If $a_n > 0$ and $\lim_{n \to \infty}{\sqrt{a_n}}>1$ show that $\lim_{n \to \infty}a_n$ exists.

Calculus problem regarding graph of derivative of a function

How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below?

Proving that euclidean distance is uniform continuous by the two variables

How can I prove the Wolfram Alpha result $\int_0^{\infty} \frac{(\sin x)^2}{x^2-\pi ^2} dx=-\frac1{2\pi}$?

how to show that $\Delta [\frac{c- |x-a|^2}{|x-b|^n}] = 2n|x-b|^{-n-2}(c-|a-b|^2), \; x \neq b$

What is the closest point to $(0,-1/2)$ on the curve $x^2+2y=0$? Why can't I differentiate over $y$?

Roots of a Quadratic Equation - Upper Bounding

what does $f''$ suggests about the graph of $f$?

Showing $\;\ln(\ln(1+\frac{1}{\vert x \vert}))\notin L^{\infty}(\{\vert x \vert \lt 1\})\;$

guessing the value based on derivative

Surface integral of spherical shell in a $e^{-x^2}$ field

Proof verification: derivative of $x^n$

Horizontal asymptotes of function defined as an inequation

When is equation has a unique solution?

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