Question

Finding a closed form for the recursively defined function using the substitution method.

score 595 · Answer 1 · 2026-05-04 18:10:01

595

Views

Finding a closed form for the recursively defined function using the substitution method.

Published on 04 May 2026 - 18:10

score 5.6k · Answer 2 · 2026-04-01 14:29:30

5.6k

Views

Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.

Published on 01 Apr 2026 - 14:29

score 63 · Answer 3 · 2026-04-17 07:55:09

63

Views

Show that the sequence $(x_n)=c^{\frac{1}{n}}$ is increasing for $0 < c < 1$.

Published on 17 Apr 2026 - 7:55

score 152 · Answer 4 · 2026-04-17 00:21:31

152

Views

Multiplying products of $p_1,p_2,\ldots,p_n$ gives a square.

Published on 17 Apr 2026 - 0:21

score 64 · Answer 5 · 2026-04-13 19:28:00

64

Views

Let $A ∈ M_{2×2}(\mathbb{C})$ be a matrix having a unique eigenvalue $c$. Show that $A^n = c^{n−1}[nA − (n − 1)cI ]$ for all $n > 0$.

Published on 13 Apr 2026 - 19:28

score 38 · Answer 6 · 2026-04-17 06:26:27

38

Views

Show that, for all $n > 0$, $A^n = {a^n\over a − b} (A − bI) + {b^n\over b − a} (A − aI)$.

Published on 17 Apr 2026 - 6:26

score 5.2k · Answer 7 · 2026-03-29 03:25:52

5.2k

Views

Mathematical Induction for $4 + 10 + 16 +…+ (6n−2) = n(3n +1)$

Published on 29 Mar 2026 - 3:25

score 131 · Answer 8 · 2026-04-16 05:08:45

131

Views

Show that $n^{n-3} \ge n!$ for n=9, 10,...

Published on 16 Apr 2026 - 5:08

score 724 · Answer 9 · 2026-04-09 04:28:36

724

Views

Prove that sum $(\sqrt2+1)^n+(\sqrt2-1)^n$ is rational for even numbers

Published on 09 Apr 2026 - 4:28

score 147 · Answer 10 · 2026-04-15 21:59:21

147

Views

Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$

Published on 15 Apr 2026 - 21:59

score 361 · Answer 11 · 2026-04-15 08:27:34

361

Views

Proof: $\sqrt[n]{n} > \sqrt[n+1]{n+1}$

Published on 15 Apr 2026 - 8:27

score 210 · Answer 12 · 2015-10-24 18:16:09

210

Views

Prove: $1+{n\choose 1}\cos\phi+{n\choose 2}\cos2\phi+...+{n\choose n}\cos n\phi=2^n\cos^n\frac{\phi}{2}\cos\frac{n\phi}{2}$

Published on 24 Oct 2015 - 18:16

score 1.8k · Answer 13 · 2026-04-14 23:23:12

1.8k

Views

Prove for any number n, it is possible to select $X = 2^n$ numbers from $2^{n+1}$ numbers s.t. the sum of X is divisible by $2^n$

Published on 14 Apr 2026 - 23:23

score 755 · Answer 14 · 2026-04-03 12:43:30

755

Views

Proving A is a subset of S by mathematical induction?

Published on 03 Apr 2026 - 12:43

score 1.1k · Answer 15 · 2026-04-09 14:43:15

1.1k

Views

How do I derive a formula for this ∏ notation?

Published on 09 Apr 2026 - 14:43

List Question

Finding a closed form for the recursively defined function using the substitution method.

Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.

Show that the sequence $(x_n)=c^{\frac{1}{n}}$ is increasing for $0 < c < 1$.

Multiplying products of $p_1,p_2,\ldots,p_n$ gives a square.

Let $A ∈ M_{2×2}(\mathbb{C})$ be a matrix having a unique eigenvalue $c$. Show that $A^n = c^{n−1}[nA − (n − 1)cI ]$ for all $n > 0$.

Show that, for all $n > 0$, $A^n = {a^n\over a − b} (A − bI) + {b^n\over b − a} (A − aI)$.

Mathematical Induction for $4 + 10 + 16 +…+ (6n−2) = n(3n +1)$

Show that $n^{n-3} \ge n!$ for n=9, 10,...

Prove that sum $(\sqrt2+1)^n+(\sqrt2-1)^n$ is rational for even numbers

Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$

Proof: $\sqrt[n]{n} > \sqrt[n+1]{n+1}$

Prove: $1+{n\choose 1}\cos\phi+{n\choose 2}\cos2\phi+...+{n\choose n}\cos n\phi=2^n\cos^n\frac{\phi}{2}\cos\frac{n\phi}{2}$

Prove for any number n, it is possible to select $X = 2^n$ numbers from $2^{n+1}$ numbers s.t. the sum of X is divisible by $2^n$

Proving A is a subset of S by mathematical induction?

How do I derive a formula for this ∏ notation?

Trending Questions

Popular # Hahtags

Popular Questions