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Solution check: summation inequality proof by induction

score 83 · Answer 1 · 2026-04-10 15:28:14

83

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Solution check: summation inequality proof by induction

Published on 10 Apr 2026 - 15:28

score 281 · Answer 2 · 2026-04-16 23:24:18

281

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proving the inequality $ (\frac{n}{e})^n \leq n! \leq en ( \frac{n}{e})^n$ by induction

Published on 16 Apr 2026 - 23:24

score 157 · Answer 3 · 2026-04-16 05:37:37

157

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By induction prove $\prod _{i=1}^{n} \frac{n+i}{2i-3} = 2^n (1 - 2n)$

Published on 16 Apr 2026 - 5:37

score 1.9k · Answer 4 · 2026-04-16 07:31:25

1.9k

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Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.

Published on 16 Apr 2026 - 7:31

score 82 · Answer 5 · 2026-04-17 10:36:30

82

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Suppose that $a, b ∈ N$ are relatively prime. Prove that, for any $k ∈ N$, $a^k$ and $b$ are relatively prime.

Published on 17 Apr 2026 - 10:36

score 126 · Answer 6 · 2026-04-11 12:09:16

126

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Mathematical proof by induction.

Published on 11 Apr 2026 - 12:09

score 67 · Answer 7 · 2026-04-16 21:29:59

67

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Hint for prove $\forall n \in \Bbb N \sum _{i=1}^{n} \frac {1}{i!} \le 2 - \frac{1}{2^{n-1}}$?

Published on 16 Apr 2026 - 21:29

score 42 · Answer 8 · 2026-04-09 20:56:29

42

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Help understanding one of Euler's theorem in Number Theory

Published on 09 Apr 2026 - 20:56

score 1.9k · Answer 9 · 2026-04-15 04:13:41

1.9k

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Why can we assume a statement is true for $n = k$, when using induction?

Published on 15 Apr 2026 - 4:13

score 1.8k · Answer 10 · 2026-04-17 04:27:42

1.8k

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Delete some numbers in $x_1+x_2+...+x_n=y_1+y_2+...+y_m<mn$

Published on 17 Apr 2026 - 4:27

score 2k · Answer 11 · 2026-04-16 00:27:11

2k

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$\sum_{k=1}^n 1/k - \log n$

Published on 16 Apr 2026 - 0:27

score 252 · Answer 12 · 2026-05-13 18:29:25

252

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Proving Recurrence Relation By Forward Substitution

Published on 13 May 2026 - 18:29

score 333 · Answer 13 · 2026-04-14 12:11:32

333

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Prove that in every WFF, there is a logical connective between every two atoms.

Published on 14 Apr 2026 - 12:11

score 214 · Answer 14 · 2026-04-15 07:38:15

214

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Proof by strong induction combinatorics problem: $1(1!) + 2(2!) + 3(3!) + \dots + n(n!) = (n+1)! - 1$

Published on 15 Apr 2026 - 7:38

score 252 · Answer 15 · 2026-04-09 16:30:38

252

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Proving running time with induction

Published on 09 Apr 2026 - 16:30

List Question

Solution check: summation inequality proof by induction

proving the inequality $ (\frac{n}{e})^n \leq n! \leq en ( \frac{n}{e})^n$ by induction

By induction prove $\prod _{i=1}^{n} \frac{n+i}{2i-3} = 2^n (1 - 2n)$

Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.

Suppose that $a, b ∈ N$ are relatively prime. Prove that, for any $k ∈ N$, $a^k$ and $b$ are relatively prime.

Mathematical proof by induction.

Hint for prove $\forall n \in \Bbb N \sum _{i=1}^{n} \frac {1}{i!} \le 2 - \frac{1}{2^{n-1}}$?

Help understanding one of Euler's theorem in Number Theory

Why can we assume a statement is true for $n = k$, when using induction?

Delete some numbers in $x_1+x_2+...+x_n=y_1+y_2+...+y_m<mn$

$\sum_{k=1}^n 1/k - \log n$

Proving Recurrence Relation By Forward Substitution

Prove that in every WFF, there is a logical connective between every two atoms.

Proof by strong induction combinatorics problem: $1(1!) + 2(2!) + 3(3!) + \dots + n(n!) = (n+1)! - 1$

Proving running time with induction

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