Question

How to prove that $\alpha^p = 1$ using induction?

score 164 · Answer 1 · 2026-03-25 17:36:25

164

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How to prove that $\alpha^p = 1$ using induction?

Published on 25 Mar 2026 - 17:36

score 97 · Answer 2 · 2026-03-25 14:25:14

97

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Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n

Published on 25 Mar 2026 - 14:25

score 135 · Answer 3 · 2026-03-24 23:43:06

135

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Why isn't $0+a=a$ something we derive?

Published on 24 Mar 2026 - 23:43

score 75 · Answer 4 · 2018-03-28 09:35:18

75

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Showing that $\int_0^{ \frac \pi 2} \cos^{2n+1}(x) dx \ = \frac{4^n(n!)²}{(2n+1)!}$?

Published on 28 Mar 2018 - 9:35

score 92 · Answer 5 · 2026-03-25 04:40:59

92

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Equivalence of $I\Sigma_n$ and $I\Pi_n$

Published on 25 Mar 2026 - 4:40

score 73 · Answer 6 · 2018-03-29 02:45:43

73

Views

Prove that $a_{n+1} = 2a_n$ for all integers n≥1. Prove that $a_n = 2^{n−1}$ for n≥1.

Published on 29 Mar 2018 - 2:45

score 67 · Answer 7 · 2018-03-30 02:46:19

67

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a specific sum of cube property(narcissistic number)

Published on 30 Mar 2018 - 2:46

score 88 · Answer 8 · 2018-03-30 08:49:25

88

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Bounds on $\frac{2n!}{(n!)^2}$

Published on 30 Mar 2018 - 8:49

score 773 · Answer 9 · 2018-03-30 10:46:35

773

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If $n\in \mathbb{N},$ then $(1-1/2) (1-1/4)(1-1/8)(1-1/16)...(1-1/2^n)\geq 1/4+1/2^{n+1}.$

Published on 30 Mar 2018 - 10:46

score 70 · Answer 10 · 2018-03-30 13:56:38

70

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how do I show this :$\sum_{k=0}^{2n }\binom{2n}{k} \sin ((n-k)x)=0$ , for every real $x$ and for every integer $n$?

Published on 30 Mar 2018 - 13:56

score 147 · Answer 11 · 2026-03-25 04:43:48

147

Views

Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.

Published on 25 Mar 2026 - 4:43

score 111 · Answer 12 · 2026-03-25 09:28:36

111

Views

Proving that for $x \neq 0$ there exists a $y$ such that $S(y) = x$.

Published on 25 Mar 2026 - 9:28

score 27 · Answer 13 · 2026-03-25 01:29:06

27

Views

Understanding how for an infinite set $a$, $h(f)=(g(f\upharpoonright n),f(n))$ defines a bijection from $^{n+1}a$ onto $a\times a$

Published on 25 Mar 2026 - 1:29

score 55 · Answer 14 · 2026-03-25 03:01:23

55

Views

Proof related to monotone functions and induction

Published on 25 Mar 2026 - 3:01

score 398 · Answer 15 · 2018-03-31 17:23:19

398

Views

Proof by induction of series summation

Published on 31 Mar 2018 - 17:23

List Question

How to prove that $\alpha^p = 1$ using induction?

Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n

Why isn't $0+a=a$ something we derive?

Showing that $\int_0^{ \frac \pi 2} \cos^{2n+1}(x) dx \ = \frac{4^n(n!)²}{(2n+1)!}$?

Equivalence of $I\Sigma_n$ and $I\Pi_n$

Prove that $a_{n+1} = 2a_n$ for all integers n≥1. Prove that $a_n = 2^{n−1}$ for n≥1.

a specific sum of cube property(narcissistic number)

Bounds on $\frac{2n!}{(n!)^2}$

If $n\in \mathbb{N},$ then $(1-1/2) (1-1/4)(1-1/8)(1-1/16)...(1-1/2^n)\geq 1/4+1/2^{n+1}.$

how do I show this :$\sum_{k=0}^{2n }\binom{2n}{k} \sin ((n-k)x)=0$ , for every real $x$ and for every integer $n$?

Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.

Proving that for $x \neq 0$ there exists a $y$ such that $S(y) = x$.

Understanding how for an infinite set $a$, $h(f)=(g(f\upharpoonright n),f(n))$ defines a bijection from $^{n+1}a$ onto $a\times a$

Proof related to monotone functions and induction

Proof by induction of series summation

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