Question

Prove by induction, that $ \sum_{i=1}^n \frac{i}{(i+1)!}= \frac{1}{(n+1)(n-1)!}$

score 100 · Answer 1 · 2026-04-16 04:32:41

100

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Prove by induction, that $ \sum_{i=1}^n \frac{i}{(i+1)!}= \frac{1}{(n+1)(n-1)!}$

Published on 16 Apr 2026 - 4:32

score 237 · Answer 2 · 2026-04-15 09:17:07

237

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Problem proving inequality $\frac{4^n}{n+1}\leq \frac{(2n)!}{(n!)^2}$

Published on 15 Apr 2026 - 9:17

score 105 · Answer 3 · 2026-04-09 16:50:03

105

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Induction proof using inequalities

Published on 09 Apr 2026 - 16:50

score 156 · Answer 4 · 2026-04-17 08:41:47

156

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Induction: $\sqrt{1+\sqrt{n+\sqrt{n^2+\sqrt{n^3+...+\sqrt{n^n}}}}} < n$

Published on 17 Apr 2026 - 8:41

score 267 · Answer 5 · 2026-04-14 07:04:17

267

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How does $\frac{-1}{k}+\frac{1}{(k+1)^2} \leq \frac{-1}{k+1}$ helps to show that $\sum\limits_{i=1}^k\frac1{i^2}\leq \ 2-\frac{1}{k}$

Published on 14 Apr 2026 - 7:04

score 489 · Answer 6 · 2026-04-08 22:48:41

489

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Proof Loop Invariant

Published on 08 Apr 2026 - 22:48

score 238 · Answer 7 · 2026-04-15 04:01:12

238

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If in all subsets of size k there exist at least one pair of elements in a relation...

Published on 15 Apr 2026 - 4:01

score 528 · Answer 8 · 2026-04-09 11:29:20

528

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Struggling to understand how to use Structural Induction to prove a recursively defined Set

Published on 09 Apr 2026 - 11:29

score 1.8k · Answer 9 · 2026-04-16 11:04:18

1.8k

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Proving n'th derivative of $\sqrt{x}$ by induction

Published on 16 Apr 2026 - 11:04

score 177 · Answer 10 · 2026-04-16 17:11:03

177

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Prove by induction $\frac{a_1+a_2+\cdots+a_n}{n}\geq 1$

Published on 16 Apr 2026 - 17:11

score 179 · Answer 11 · 2026-04-15 07:01:59

179

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How to prove $47 \mid 49^{n} - 2^n $ by induction

Published on 15 Apr 2026 - 7:01

score 229 · Answer 12 · 2026-04-11 16:09:57

229

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Proving well formed propositional statements have well defined truth values

Published on 11 Apr 2026 - 16:09

score 174 · Answer 13 · 2026-04-15 12:39:43

174

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Prove $x>nδ_n$, $\forall n∈\mathbb{N}+$ for $δ_n := \sqrt[n]{x}−1$

Published on 15 Apr 2026 - 12:39

score 1.7k · Answer 14 · 2026-04-17 08:14:37

1.7k

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Show by induction that 2^n > n for all integers n > 0

Published on 17 Apr 2026 - 8:14

score 255 · Answer 15 · 2026-04-12 18:46:27

255

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Induction of infinite series

Published on 12 Apr 2026 - 18:46

List Question

Prove by induction, that $ \sum_{i=1}^n \frac{i}{(i+1)!}= \frac{1}{(n+1)(n-1)!}$

Problem proving inequality $\frac{4^n}{n+1}\leq \frac{(2n)!}{(n!)^2}$

Induction proof using inequalities

Induction: $\sqrt{1+\sqrt{n+\sqrt{n^2+\sqrt{n^3+...+\sqrt{n^n}}}}} < n$

How does $\frac{-1}{k}+\frac{1}{(k+1)^2} \leq \frac{-1}{k+1}$ helps to show that $\sum\limits_{i=1}^k\frac1{i^2}\leq \ 2-\frac{1}{k}$

Proof Loop Invariant

If in all subsets of size k there exist at least one pair of elements in a relation...

Struggling to understand how to use Structural Induction to prove a recursively defined Set

Proving n'th derivative of $\sqrt{x}$ by induction

Prove by induction $\frac{a_1+a_2+\cdots+a_n}{n}\geq 1$

How to prove $47 \mid 49^{n} - 2^n $ by induction

Proving well formed propositional statements have well defined truth values

Prove $x>nδ_n$, $\forall n∈\mathbb{N}+$ for $δ_n := \sqrt[n]{x}−1$

Show by induction that 2^n > n for all integers n > 0

Induction of infinite series

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