Question

If $a$, $b$, $c$ are three positive numbers in harmonic sequence, show that $a^2+c^2>2b^2$.

score 2.5k · Answer 1 · 2026-03-25 03:02:05

2.5k

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If $a$, $b$, $c$ are three positive numbers in harmonic sequence, show that $a^2+c^2>2b^2$.

Published on 25 Mar 2026 - 3:02

score 336 · Answer 2 · 2026-03-25 01:20:28

336

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Find the sum to $n$ terms of the following series

Published on 25 Mar 2026 - 1:20

score 329 · Answer 3 · 2026-03-23 16:48:58

329

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Find the $n^{th}$ term and the sum to $n$ terms of the following series

Published on 23 Mar 2026 - 16:48

score 84 · Answer 4 · 2026-03-24 11:36:34

84

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Non-overlapping arithmetic progressions in $\mathbb{Z}_N$

Published on 24 Mar 2026 - 11:36

score 139 · Answer 5 · 2026-03-24 05:30:21

139

Views

A nowhere dense set containing arbitrarily close arithmetic progressions

Published on 24 Mar 2026 - 5:30

score 100 · Answer 6 · 2026-03-24 06:44:36

100

Views

arithmetic sequence (Algebra 1, Khan Academy)

Published on 24 Mar 2026 - 6:44

score 222 · Answer 7 · 2026-03-23 07:42:25

222

Views

On the least prime in an arithmetic progression $a + nb$ where $a,b$ are distinct primes.

Published on 23 Mar 2026 - 7:42

score 1.7k · Answer 8 · 2026-03-24 11:28:29

If $x,y,z$ are three natural numbers are in A.P. and $x+y+z=21$ then the possible number of values of the ordered triplet $(x,y,z)$ is

score 2.7k · Answer 9 · 2026-03-24 14:50:39

2.7k

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If $a,b,c$ are in $A.P.$ then prove that $b^2>ac$

Published on 24 Mar 2026 - 14:50

score 276 · Answer 10 · 2026-03-24 08:46:05

276

Views

Prerequisites to tackle Multiplicative number theory (Dirichlet theorem on arithmetic progressions)

Published on 24 Mar 2026 - 8:46

score 105 · Answer 11 · 2026-03-25 04:39:00

105

Views

What type of sequences would these be?

Published on 25 Mar 2026 - 4:39

score 409 · Answer 12 · 2026-03-23 22:09:29

409

Views

Show that $\mathbb{Z}$ with the Furstenberg's topology is compact

Published on 23 Mar 2026 - 22:09

score 942 · Answer 13 · 2026-03-25 01:14:12

942

Views

Arithmetic and Geometric Sequences Relationship

Published on 25 Mar 2026 - 1:14

score 325 · Answer 14 · 2026-03-24 03:46:55

325

Views

If the sides $a$, $b$ and $c$ of $\triangle ABC$ are in Arithmetic Progression

Published on 24 Mar 2026 - 3:46

score 44 · Answer 15 · 2026-03-23 19:22:28

44

Views

What are the numbers present in the following Arithmetic Progression?

Published on 23 Mar 2026 - 19:22

List Question

If $a$, $b$, $c$ are three positive numbers in harmonic sequence, show that $a^2+c^2>2b^2$.

Find the sum to $n$ terms of the following series

Find the $n^{th}$ term and the sum to $n$ terms of the following series

Non-overlapping arithmetic progressions in $\mathbb{Z}_N$

A nowhere dense set containing arbitrarily close arithmetic progressions

arithmetic sequence (Algebra 1, Khan Academy)

On the least prime in an arithmetic progression $a + nb$ where $a,b$ are distinct primes.

If $x,y,z$ are three natural numbers are in A.P. and $x+y+z=21$ then the possible number of values of the ordered triplet $(x,y,z)$ is

If $a,b,c$ are in $A.P.$ then prove that $b^2>ac$

Prerequisites to tackle Multiplicative number theory (Dirichlet theorem on arithmetic progressions)

What type of sequences would these be?

Show that $\mathbb{Z}$ with the Furstenberg's topology is compact

Arithmetic and Geometric Sequences Relationship

If the sides $a$, $b$ and $c$ of $\triangle ABC$ are in Arithmetic Progression

What are the numbers present in the following Arithmetic Progression?

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