Question

how to prove by induction the $ (1+x)^{n}>1+nx+nx^2$

score 89 · Answer 1 · 2026-04-17 15:04:30

89

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how to prove by induction the $ (1+x)^{n}>1+nx+nx^2$

Published on 17 Apr 2026 - 15:04

score 4.3k · Answer 2 · 2026-04-09 06:45:53

4.3k

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Proof without using induction

Published on 09 Apr 2026 - 6:45

score 132 · Answer 3 · 2026-04-15 11:53:56

132

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Using induction prove $\sum\limits_{k=1}^n\binom{k}{k-1}=\binom{n+1}{n-1}$

Published on 15 Apr 2026 - 11:53

score 2k · Answer 4 · 2026-04-13 15:28:43

2k

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Show that there exists a unique function with a certain property

Published on 13 Apr 2026 - 15:28

score 51 · Answer 5 · 2026-04-16 13:52:56

51

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How to show $(1+a)^n<1+2^n a$ for all $n\in\mathbb N$ and $a\in (0, 1)$?

Published on 16 Apr 2026 - 13:52

score 4.1k · Answer 6 · 2026-04-14 13:38:46

4.1k

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Prove that Euclid's algorithm computes the GCD of any pair of nonnegative integers

Published on 14 Apr 2026 - 13:38

score 67 · Answer 7 · 2026-04-10 18:25:33

67

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simplifying equations

Published on 10 Apr 2026 - 18:25

score 4.1k · Answer 8 · 2026-04-14 18:22:53

4.1k

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Proving that $12^n + 2(5^{n-1})$ is a multiple of 7 for $n\geq 1$ by induction

Published on 14 Apr 2026 - 18:22

score 808 · Answer 9 · 2026-04-14 23:47:00

808

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Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.

Published on 14 Apr 2026 - 23:47

score 1.9k · Answer 10 · 2026-04-13 06:35:59

1.9k

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Is there a standard name for this "continuous induction" principle?

Published on 13 Apr 2026 - 6:35

score 606 · Answer 11 · 2026-04-16 08:51:07

606

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Proving that there exists a horizontal chord with length $1/n$ for a continuous function $f: [0,1] \to \mathbb R$

Published on 16 Apr 2026 - 8:51

score 97 · Answer 12 · 2026-04-16 10:57:38

97

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Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$

Published on 16 Apr 2026 - 10:57

score 92 · Answer 13 · 2026-04-11 05:49:16

How do I use the principle of mathematical induction to prove whether or not $\sum_{k=1}^n (-1)^k = \frac{(-1)^n-1}2$ is a true statement?

score 358 · Answer 14 · 2026-04-14 16:26:24

358

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The necessity of the axiom of induction

Published on 14 Apr 2026 - 16:26

score 505 · Answer 15 · 2026-04-10 14:33:46

505

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Help with induction step of proving a recursive definition / sequence

Published on 10 Apr 2026 - 14:33

List Question

how to prove by induction the $ (1+x)^{n}>1+nx+nx^2$

Proof without using induction

Using induction prove $\sum\limits_{k=1}^n\binom{k}{k-1}=\binom{n+1}{n-1}$

Show that there exists a unique function with a certain property

How to show $(1+a)^n<1+2^n a$ for all $n\in\mathbb N$ and $a\in (0, 1)$?

Prove that Euclid's algorithm computes the GCD of any pair of nonnegative integers

simplifying equations

Proving that $12^n + 2(5^{n-1})$ is a multiple of 7 for $n\geq 1$ by induction

Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.

Is there a standard name for this "continuous induction" principle?

Proving that there exists a horizontal chord with length $1/n$ for a continuous function $f: [0,1] \to \mathbb R$

Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$

How do I use the principle of mathematical induction to prove whether or not $\sum_{k=1}^n (-1)^k = \frac{(-1)^n-1}2$ is a true statement?

The necessity of the axiom of induction

Help with induction step of proving a recursive definition / sequence

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