Question

How to show that for sequence $x_1=2$, and $x_{n+1}=\frac12\big(x_n+\frac2{x_n}\big)$; for all $n$, $(x_n)^2>2$?

score 173 · Answer 1 · 2026-04-16 08:16:03

173

Views

How to show that for sequence $x_1=2$, and $x_{n+1}=\frac12\big(x_n+\frac2{x_n}\big)$; for all $n$, $(x_n)^2>2$?

Published on 16 Apr 2026 - 8:16

score 227 · Answer 2 · 2026-04-13 17:03:37

227

Views

Can't find the mistake in my inductive step

Published on 13 Apr 2026 - 17:03

score 104 · Answer 3 · 2026-04-16 21:33:14

104

Views

How to prove the number of all maps of the kind $f : \{1, 2, ..., n\} \to \{1, 2\}$ is $2^n$, for all $n \in\mathbb{N}$?

Published on 16 Apr 2026 - 21:33

score 53 · Answer 4 · 2026-04-11 17:37:03

53

Views

Inequality Induction Proof sufficient argument?

Published on 11 Apr 2026 - 17:37

score 296 · Answer 5 · 2026-04-10 17:16:15

296

Views

Compatibility Lemma of First-Order Languages

Published on 10 Apr 2026 - 17:16

score 415 · Answer 6 · 2026-04-09 07:55:36

415

Views

Proof by strong induction question

Published on 09 Apr 2026 - 7:55

score 298 · Answer 7 · 2026-04-11 07:58:38

298

Views

How to count number of matchings?

Published on 11 Apr 2026 - 7:58

score 76 · Answer 8 · 2026-04-17 08:35:23

76

Views

How to solve $\binom{n+m}{k} = \sum_{i=0}^{k} \binom{m}{i} \binom{n}{k-i} $

Published on 17 Apr 2026 - 8:35

score 739 · Answer 9 · 2026-04-13 17:15:19

739

Views

Induction to prove $a_n=2^n+1$

Published on 13 Apr 2026 - 17:15

score 46 · Answer 10 · 2026-04-15 02:20:02

Show that there exist rational numbers $a_{r1},...,a_{rr}$ such that $\sum_{k=1}^{n} k^{r} = \frac{1}{r+1}n^{r+1}+a_{rr}n^r+...+a_{r1}n$

score 617 · Answer 11 · 2026-04-12 06:21:53

617

Views

Stirling Number of second kind (unsigned) and binomial coefficient, proof of equality?

Published on 12 Apr 2026 - 6:21

score 386 · Answer 12 · 2026-04-15 13:15:59

386

Views

Induction proof for an inequality with a recursive formula $a_n = a_{\lfloor{n/2}\rfloor} + a_{\lceil{n/2}\rceil} + 3n + 1$

Published on 15 Apr 2026 - 13:15

score 582 · Answer 13 · 2026-04-16 05:38:35

582

Views

Prove that if sum of components of one vector adds up to 1 then the sum of the squares of the same vector is at least 1/n

Published on 16 Apr 2026 - 5:38

score 7.4k · Answer 14 · 2026-04-15 22:46:44

7.4k

Views

Proving $\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}{6}$ with Induction

Published on 15 Apr 2026 - 22:46

score 56 · Answer 15 · 2026-04-16 07:23:18

56

Views

Problem with induction of $a_{n+1} = (a_n^2 + 12)/7$

Published on 16 Apr 2026 - 7:23

List Question

How to show that for sequence $x_1=2$, and $x_{n+1}=\frac12\big(x_n+\frac2{x_n}\big)$; for all $n$, $(x_n)^2>2$?

Can't find the mistake in my inductive step

How to prove the number of all maps of the kind $f : \{1, 2, ..., n\} \to \{1, 2\}$ is $2^n$, for all $n \in\mathbb{N}$?

Inequality Induction Proof sufficient argument?

Compatibility Lemma of First-Order Languages

Proof by strong induction question

How to count number of matchings?

How to solve $\binom{n+m}{k} = \sum_{i=0}^{k} \binom{m}{i} \binom{n}{k-i} $

Induction to prove $a_n=2^n+1$

Show that there exist rational numbers $a_{r1},...,a_{rr}$ such that $\sum_{k=1}^{n} k^{r} = \frac{1}{r+1}n^{r+1}+a_{rr}n^r+...+a_{r1}n$

Stirling Number of second kind (unsigned) and binomial coefficient, proof of equality?

Induction proof for an inequality with a recursive formula $a_n = a_{\lfloor{n/2}\rfloor} + a_{\lceil{n/2}\rceil} + 3n + 1$

Prove that if sum of components of one vector adds up to 1 then the sum of the squares of the same vector is at least 1/n

Proving $\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}{6}$ with Induction

Problem with induction of $a_{n+1} = (a_n^2 + 12)/7$

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