Question

evaluating the limit $\lim \limits_{n \to \infty} \frac{(4(n*3^n + 3))^n}{(3^{n+1} (n+1)+3)^{n+1}}$

score 88 · Answer 1 · 2026-04-16 08:17:09

88

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evaluating the limit $\lim \limits_{n \to \infty} \frac{(4(n*3^n + 3))^n}{(3^{n+1} (n+1)+3)^{n+1}}$

Published on 16 Apr 2026 - 8:17

score 142 · Answer 2 · 2026-04-15 19:29:28

142

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How does $(n+1)! - 1 + (n+1)(n+1)! = (n+1)!(1+n+1) - 1$?

Published on 15 Apr 2026 - 19:29

score 178 · Answer 3 · 2026-04-13 21:28:30

178

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Prove by induction that $(1-a)^n ≥ 1-na$, $∀ n≥1$ for appropriate $a$.

Published on 13 Apr 2026 - 21:28

score 592 · Answer 4 · 2026-04-14 04:07:25

592

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Show that a set of connectives {∨, ∧} through structural induction is not a complete set of connectives

Published on 14 Apr 2026 - 4:07

score 66 · Answer 5 · 2015-12-14 23:47:08

66

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Prove using the binomial theorem that $(1+\frac{1}{n})^n < \sum_{j=0}^n \frac{1}{j!} < 2 + \frac{1}{2} + \frac{1}{4} + ...+ \frac{1}{2^{n-1}}$

Published on 14 Dec 2015 - 23:47

score 52 · Answer 6 · 2026-04-14 20:13:57

Prove by induction that $\sum_{k=n+1}^{2n} \frac{1}{k} = \sum_{m=1}^{2n} \frac{(-1)^{m+1}}{m}, \qquad \forall n \in N$

score 155 · Answer 7 · 2026-04-15 13:54:39

155

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Given a polynomial $p$, then $\forall K>0$, $\exists r_k$ such that $|t|\geq r_k \Rightarrow |p(t)|\geq K$

Published on 15 Apr 2026 - 13:54

score 1.2k · Answer 8 · 2026-04-13 18:45:32

1.2k

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How do you select base-cases for this proof?

Published on 13 Apr 2026 - 18:45

score 119 · Answer 9 · 2026-04-14 20:31:59

119

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Proving an inequality using mathematical induction

Published on 14 Apr 2026 - 20:31

score 82 · Answer 10 · 2026-04-12 22:21:57

82

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Inductive proof of 2|($n^2$ +3n + 2) if n is a natural number

Published on 12 Apr 2026 - 22:21

score 510 · Answer 11 · 2026-04-15 10:24:45

510

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Give a recursive definition for the set T.

Published on 15 Apr 2026 - 10:24

score 121 · Answer 12 · 2026-04-15 16:55:48

121

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Show by induction that $(n^2) + 1 < 2^n$ for intergers $n > 4$

Published on 15 Apr 2026 - 16:55

score 116 · Answer 13 · 2026-04-16 02:21:33

116

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How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?

Published on 16 Apr 2026 - 2:21

score 182 · Answer 14 · 2026-04-12 01:46:08

182

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Inductive Proof of $n! < n^n$

Published on 12 Apr 2026 - 1:46

score 38 · Answer 15 · 2026-04-14 07:33:02

38

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Mathematical induction divisibility

Published on 14 Apr 2026 - 7:33

List Question

evaluating the limit $\lim \limits_{n \to \infty} \frac{(4(n*3^n + 3))^n}{(3^{n+1} (n+1)+3)^{n+1}}$

How does $(n+1)! - 1 + (n+1)(n+1)! = (n+1)!(1+n+1) - 1$?

Prove by induction that $(1-a)^n ≥ 1-na$, $∀ n≥1$ for appropriate $a$.

Show that a set of connectives {∨, ∧} through structural induction is not a complete set of connectives

Prove using the binomial theorem that $(1+\frac{1}{n})^n < \sum_{j=0}^n \frac{1}{j!} < 2 + \frac{1}{2} + \frac{1}{4} + ...+ \frac{1}{2^{n-1}}$

Prove by induction that $\sum_{k=n+1}^{2n} \frac{1}{k} = \sum_{m=1}^{2n} \frac{(-1)^{m+1}}{m}, \qquad \forall n \in N$

Given a polynomial $p$, then $\forall K>0$, $\exists r_k$ such that $|t|\geq r_k \Rightarrow |p(t)|\geq K$

How do you select base-cases for this proof?

Proving an inequality using mathematical induction

Inductive proof of 2|($n^2$ +3n + 2) if n is a natural number

Give a recursive definition for the set T.

Show by induction that $(n^2) + 1 < 2^n$ for intergers $n > 4$

How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?

Inductive Proof of $n! < n^n$

Mathematical induction divisibility

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