Question

Have some trouble proving $(1-x)^n \geq 1-nx$

score 64 · Answer 1 · 2026-04-14 22:03:25

64

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Have some trouble proving $(1-x)^n \geq 1-nx$

Published on 14 Apr 2026 - 22:03

score 372 · Answer 2 · 2026-04-16 01:19:22

372

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Induction proof: $(x_{1}+x_{2}+...+x_{n})^2\leqslant n(x_{1}^2+x_{2}^2+...+x_{n}^2)$

Published on 16 Apr 2026 - 1:19

score 75 · Answer 3 · 2026-04-16 07:02:54

75

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Prove: $ 1\times3 +2\times4 + \cdots + n(n+2) = \frac{1}{6} \times n(n+1)(2n+7)$ using Induction

Published on 16 Apr 2026 - 7:02

score 331 · Answer 4 · 2026-04-16 14:28:52

331

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Prove that: $2^n < n!$ Using Induction

Published on 16 Apr 2026 - 14:28

score 93 · Answer 5 · 2026-04-14 23:02:51

93

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proving $E \leq \frac{(n-k+1) \cdot (n-k)}{2}$

Published on 14 Apr 2026 - 23:02

score 163 · Answer 6 · 2026-04-09 10:48:48

163

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Proof strategy for propositional logic algorithm

Published on 09 Apr 2026 - 10:48

score 2.9k · Answer 7 · 2026-04-16 02:32:10

2.9k

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Suppose $a \in \mathbb{Z}.$ Prove that $5 \mid 2^na$ implies $5 \mid a$ for any $n \in \mathbb{N}$

Published on 16 Apr 2026 - 2:32

score 130 · Answer 8 · 2026-04-10 17:06:38

130

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Standard proof of permutations of $n$ people standing in line

Published on 10 Apr 2026 - 17:06

score 221 · Answer 9 · 2026-04-04 12:00:48

221

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Prove $\frac{1\cdot 3\cdots(2n-1)}{2\cdot 4 \cdots(2n)}<\frac{1}{\sqrt{2n+1}}$, $n\ge 1$

Published on 04 Apr 2026 - 12:00

score 105 · Answer 10 · 2026-04-16 03:39:26

105

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Prove that for all $n \gt 1$ $\lim_{r \to 1} \frac {r^n-1}{r-1} = n$

Published on 16 Apr 2026 - 3:39

score 131 · Answer 11 · 2026-04-11 04:19:27

131

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Induction with binomial coefficient

Published on 11 Apr 2026 - 4:19

score 125 · Answer 12 · 2026-04-10 03:37:27

125

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Proof by induction to prove an inequality help?

Published on 10 Apr 2026 - 3:37

score 3.5k · Answer 13 · 2026-04-15 02:28:36

3.5k

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induction to prove the equation $3 + 9 + 15 + ... + (6n - 3) = 3n^2$

Published on 15 Apr 2026 - 2:28

score 140 · Answer 14 · 2026-04-16 17:12:17

140

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Prove $\log(x)^{10} < x$ (for $x > 10^{10}$)

Published on 16 Apr 2026 - 17:12

score 2.7k · Answer 15 · 2026-04-11 18:57:22

2.7k

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Proving by induction that a balanced strings of parentheses has equally many opening and closing parentheses

Published on 11 Apr 2026 - 18:57

List Question

Have some trouble proving $(1-x)^n \geq 1-nx$

Induction proof: $(x_{1}+x_{2}+...+x_{n})^2\leqslant n(x_{1}^2+x_{2}^2+...+x_{n}^2)$

Prove: $ 1\times3 +2\times4 + \cdots + n(n+2) = \frac{1}{6} \times n(n+1)(2n+7)$ using Induction

Prove that: $2^n < n!$ Using Induction

proving $E \leq \frac{(n-k+1) \cdot (n-k)}{2}$

Proof strategy for propositional logic algorithm

Suppose $a \in \mathbb{Z}.$ Prove that $5 \mid 2^na$ implies $5 \mid a$ for any $n \in \mathbb{N}$

Standard proof of permutations of $n$ people standing in line

Prove $\frac{1\cdot 3\cdots(2n-1)}{2\cdot 4 \cdots(2n)}<\frac{1}{\sqrt{2n+1}}$, $n\ge 1$

Prove that for all $n \gt 1$ $\lim_{r \to 1} \frac {r^n-1}{r-1} = n$

Induction with binomial coefficient

Proof by induction to prove an inequality help?

induction to prove the equation $3 + 9 + 15 + ... + (6n - 3) = 3n^2$

Prove $\log(x)^{10} < x$ (for $x > 10^{10}$)

Proving by induction that a balanced strings of parentheses has equally many opening and closing parentheses

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