Question

How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.

score 905 · Answer 1 · 2026-04-12 23:22:06

905

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How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.

Published on 12 Apr 2026 - 23:22

score 124 · Answer 2 · 2026-04-15 18:11:58

124

Views

Prove with induction that $\sum_{k=0}^{n-1}x^{k}=\frac{x^n-1}{x-1}$

Published on 15 Apr 2026 - 18:11

score 303 · Answer 3 · 2026-04-13 14:29:55

303

Views

I'm having trouble understanding why inductive proofs are logical

Published on 13 Apr 2026 - 14:29

score 137 · Answer 4 · 2026-04-11 11:19:11

137

Views

Mathematical Induction with series and factorials.

Published on 11 Apr 2026 - 11:19

score 72 · Answer 5 · 2026-03-27 01:46:48

72

Views

The analytic extension of $\sum_{k=1}^n\frac1k$ and an induction

Published on 27 Mar 2026 - 1:46

score 75 · Answer 6 · 2026-04-16 12:48:52

75

Views

How to demonstrate that $2^{2^n - 2} + 1$ is a nonprime number?

Published on 16 Apr 2026 - 12:48

score 200 · Answer 7 · 2026-03-29 11:02:40

200

Views

Find the mistake of the following inductive proof: all algorithms have the same time complexity

Published on 29 Mar 2026 - 11:02

score 772 · Answer 8 · 2026-04-16 03:17:10

772

Views

Showing that $\sum_{j=0}^n (j+1) =\frac{(n+1) (n+2)}{2}$ whenever $n$ is a nonnegative integer.

Published on 16 Apr 2026 - 3:17

score 14.8k · Answer 9 · 2026-04-15 23:47:30

14.8k

Views

Let $G$ be a graph with $n$ vertices where every vertex has a degree of at least $\frac{n}{2}$. Prove that G is connected.

Published on 15 Apr 2026 - 23:47

score 5.1k · Answer 10 · 2026-04-11 00:14:12

5.1k

Views

Induction Proof of Taylor Series Formula

Published on 11 Apr 2026 - 0:14

score 675 · Answer 11 · 2026-03-28 02:09:18

675

Views

Induction with Turing machines.

Published on 28 Mar 2026 - 2:09

score 50 · Answer 12 · 2026-04-14 19:24:44

50

Views

In a directed graph with n≥2 nodes, if two different nodes reaches every nodes (including itself), then this graph is strongly connected.

Published on 14 Apr 2026 - 19:24

score 224 · Answer 13 · 2026-04-15 21:17:13

224

Views

Proving by induction that $n! < (\frac{n+1}{2})^n$

Published on 15 Apr 2026 - 21:17

score 38.8k · Answer 14 · 2026-04-14 03:57:45

38.8k

Views

Use mathematical induction to prove that $n^ 3 − n$ is divisible by 3 whenever n is a positive integer.

Published on 14 Apr 2026 - 3:57

score 239 · Answer 15 · 2026-03-29 11:41:31

239

Views

Arithmetic sequence whose any five consecutive elements contain a prime

Published on 29 Mar 2026 - 11:41

List Question

How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.

Prove with induction that $\sum_{k=0}^{n-1}x^{k}=\frac{x^n-1}{x-1}$

I'm having trouble understanding why inductive proofs are logical

Mathematical Induction with series and factorials.

The analytic extension of $\sum_{k=1}^n\frac1k$ and an induction

How to demonstrate that $2^{2^n - 2} + 1$ is a nonprime number?

Find the mistake of the following inductive proof: all algorithms have the same time complexity

Showing that $\sum_{j=0}^n (j+1) =\frac{(n+1) (n+2)}{2}$ whenever $n$ is a nonnegative integer.

Let $G$ be a graph with $n$ vertices where every vertex has a degree of at least $\frac{n}{2}$. Prove that G is connected.

Induction Proof of Taylor Series Formula

Induction with Turing machines.

In a directed graph with n≥2 nodes, if two different nodes reaches every nodes (including itself), then this graph is strongly connected.

Proving by induction that $n! < (\frac{n+1}{2})^n$

Use mathematical induction to prove that $n^ 3 − n$ is divisible by 3 whenever n is a positive integer.

Arithmetic sequence whose any five consecutive elements contain a prime

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