Question

Proof by induction summation

score 226 · Answer 1 · 2026-03-25 12:30:32

226

Views

Proof by induction summation

Published on 25 Mar 2026 - 12:30

score 2.5k · Answer 2 · 2026-03-25 23:42:14

2.5k

Views

Prove by induction that $\sum _{r=1}^n \cos((2r-1)\theta) = \frac{\sin(2n\theta)}{2\sin\theta}$ is true $\forall \ n \in \mathbb{Z^+}$

Published on 25 Mar 2026 - 23:42

score 56 · Answer 3 · 2026-03-30 11:59:25

56

Views

Proof $C_h = \binom{2^h-2}{2^{h-1}-1} C_{h-1}^2$ can be written non-recursively as $C_h = \frac{(2^h-1)!}{\prod_{k=1}^h (2^k-1)^{2^{h-k}}}. $

Published on 30 Mar 2026 - 11:59

score 75 · Answer 4 · 2019-06-06 13:35:05

75

Views

Proving an equality of two sums using induction for $n \in \mathbb N$

Published on 06 Jun 2019 - 13:35

score 142 · Answer 5 · 2019-06-06 15:54:34

142

Views

Prove that $\sum_{k=0}^{n}{\frac{1}{k!}}\leq 3$ $\forall n\in \mathbb{N}$

Published on 06 Jun 2019 - 15:54

score 933 · Answer 6 · 2019-06-07 07:22:18

933

Views

Induction with nth root of n

Published on 07 Jun 2019 - 7:22

score 88 · Answer 7 · 2026-03-26 02:58:26

88

Views

Taking a natural number different from zero as a base case in an inductive proof

Published on 26 Mar 2026 - 2:58

score 1.4k · Answer 8 · 2019-06-10 22:40:20

1.4k

Views

How to define induction in set theory?

Published on 10 Jun 2019 - 22:40

score 159 · Answer 9 · 2019-06-11 01:16:07

159

Views

Prove that $5^n + 6^n -1$ is divisble by 10 for all positive integers n.

Published on 11 Jun 2019 - 1:16

score 940 · Answer 10 · 2019-06-11 14:24:39

940

Views

Inductive proof that an n-cube is bipartite

Published on 11 Jun 2019 - 14:24

score 39 · Answer 11 · 2019-06-12 06:18:06

Whats an example of a predicate where if $P(1)$ is False, and $(\forall k\geq 1)(P(k)\implies P(k+1))$ is True for all natural numbers

score 72 · Answer 12 · 2019-06-12 08:21:38

72

Views

Prove using induction $\prod_{i=1}^n (1-2^{-i}) ≥ \frac{1}{4} + 2^{-(n+1)}$ for all n∈N

Published on 12 Jun 2019 - 8:21

score 84 · Answer 13 · 2019-06-12 18:23:47

84

Views

Induction: Confused by trivial proof & upper and lower index

Published on 12 Jun 2019 - 18:23

score 98 · Answer 14 · 2026-03-30 12:01:51

98

Views

Finding proof of sum of products of binomial coefficients.

Published on 30 Mar 2026 - 12:01

score 681 · Answer 15 · 2019-06-13 00:54:57

681

Views

Find all natural numbers n so that $ n^3 +(n+1)^3 >(n+2)^3$

Published on 13 Jun 2019 - 0:54

List Question

Proof by induction summation

Prove by induction that $\sum _{r=1}^n \cos((2r-1)\theta) = \frac{\sin(2n\theta)}{2\sin\theta}$ is true $\forall \ n \in \mathbb{Z^+}$

Proof $C_h = \binom{2^h-2}{2^{h-1}-1} C_{h-1}^2$ can be written non-recursively as $C_h = \frac{(2^h-1)!}{\prod_{k=1}^h (2^k-1)^{2^{h-k}}}. $

Proving an equality of two sums using induction for $n \in \mathbb N$

Prove that $\sum_{k=0}^{n}{\frac{1}{k!}}\leq 3$ $\forall n\in \mathbb{N}$

Induction with nth root of n

Taking a natural number different from zero as a base case in an inductive proof

How to define induction in set theory?

Prove that $5^n + 6^n -1$ is divisble by 10 for all positive integers n.

Inductive proof that an n-cube is bipartite

Whats an example of a predicate where if $P(1)$ is False, and $(\forall k\geq 1)(P(k)\implies P(k+1))$ is True for all natural numbers

Prove using induction $\prod_{i=1}^n (1-2^{-i}) ≥ \frac{1}{4} + 2^{-(n+1)}$ for all n∈N

Induction: Confused by trivial proof & upper and lower index

Finding proof of sum of products of binomial coefficients.

Find all natural numbers n so that $ n^3 +(n+1)^3 >(n+2)^3$

Trending Questions

Popular # Hahtags

Popular Questions