Question

if all roots of polynomial $ax^n+bx^{n-1}+cx^{n-2}+\dots+a_1x+a_0$ are real numbers, prove $b^2 - \frac{2n}{n-1}ac\ge0$

score 115 · Answer 1 · 2026-04-16 00:22:16

115

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if all roots of polynomial $ax^n+bx^{n-1}+cx^{n-2}+\dots+a_1x+a_0$ are real numbers, prove $b^2 - \frac{2n}{n-1}ac\ge0$

Published on 16 Apr 2026 - 0:22

score 91 · Answer 2 · 2026-04-13 20:16:27

91

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Closed form for $\sum_{k=0}^{j}\binom{n}{k}^2 x^k$

Published on 13 Apr 2026 - 20:16

score 73 · Answer 3 · 2026-04-15 11:31:31

73

Views

Prove by induction on the length of the walk that whenever it visits a vertex, it has traversed an odd number of edges incident to it

Published on 15 Apr 2026 - 11:31

score 99 · Answer 4 · 2026-04-12 09:52:43

99

Views

Proof by induction confusion

Published on 12 Apr 2026 - 9:52

score 57 · Answer 5 · 2026-04-14 00:34:25

57

Views

Use induction to find a number, rather then proving an assumption

Published on 14 Apr 2026 - 0:34

score 478 · Answer 6 · 2026-04-11 11:35:21

478

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What do we assume when we do proof by induction?

Published on 11 Apr 2026 - 11:35

score 104 · Answer 7 · 2026-04-11 19:16:47

104

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Exercise 1.26 from Riley's "Mathematical Methods for Physics and Engineering" concerning proof by induction

Published on 11 Apr 2026 - 19:16

score 43 · Answer 8 · 2026-04-12 10:21:48

43

Views

How to prove that finite induction implies complete finite induction?

Published on 12 Apr 2026 - 10:21

score 42 · Answer 9 · 2026-04-10 05:49:11

42

Views

Induction strategy with mathematical symbols

Published on 10 Apr 2026 - 5:49

score 104 · Answer 10 · 2026-04-10 21:08:12

104

Views

Antimagic square induction problem

Published on 10 Apr 2026 - 21:08

score 38 · Answer 11 · 2026-04-13 23:50:36

38

Views

Showing that a series of sets are cumulative by induction

Published on 13 Apr 2026 - 23:50

score 69 · Answer 12 · 2026-04-16 08:33:41

69

Views

Prove $\sum_{k=1}^{2n-1} \frac{(-1)^{k + 1}}{k} = \sum_{k=n}^{2n-1} \frac{1}{k}$ by induction

Published on 16 Apr 2026 - 8:33

score 145 · Answer 13 · 2026-04-16 06:41:44

145

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How can I prove $\left(1+{1\over n}\right)^{n}\le\left(1+{1\over 1+n}\right)^{n+1}$ via induction?

Published on 16 Apr 2026 - 6:41

score 36 · Answer 14 · 2026-04-25 16:55:01

36

Views

Evaluation of an indexed sum.

Published on 25 Apr 2026 - 16:55

score 39 · Answer 15 · 2026-04-09 19:42:39

39

Views

Checking an induction proof for a summation.

Published on 09 Apr 2026 - 19:42

List Question

if all roots of polynomial $ax^n+bx^{n-1}+cx^{n-2}+\dots+a_1x+a_0$ are real numbers, prove $b^2 - \frac{2n}{n-1}ac\ge0$

Closed form for $\sum_{k=0}^{j}\binom{n}{k}^2 x^k$

Prove by induction on the length of the walk that whenever it visits a vertex, it has traversed an odd number of edges incident to it

Proof by induction confusion

Use induction to find a number, rather then proving an assumption

What do we assume when we do proof by induction?

Exercise 1.26 from Riley's "Mathematical Methods for Physics and Engineering" concerning proof by induction

How to prove that finite induction implies complete finite induction?

Induction strategy with mathematical symbols

Antimagic square induction problem

Showing that a series of sets are cumulative by induction

Prove $\sum_{k=1}^{2n-1} \frac{(-1)^{k + 1}}{k} = \sum_{k=n}^{2n-1} \frac{1}{k}$ by induction

How can I prove $\left(1+{1\over n}\right)^{n}\le\left(1+{1\over 1+n}\right)^{n+1}$ via induction?

Evaluation of an indexed sum.

Checking an induction proof for a summation.

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