Question

Given the recurrence $T_n = 2T_{n-1} - T_{n-2}$, prove by Induction that $T_n = n$

score 212 · Answer 1 · 2026-05-14 03:20:21

212

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Given the recurrence $T_n = 2T_{n-1} - T_{n-2}$, prove by Induction that $T_n = n$

Published on 14 May 2026 - 3:20

score 632 · Answer 2 · 2026-04-15 10:41:51

632

Views

Mathematical induction proof problem: $\sum_{i=1}^{n-1} i(i+1) = \frac{n(n+1)(n-1)}3$

Published on 15 Apr 2026 - 10:41

score 51 · Answer 3 · 2026-04-11 04:08:46

51

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Proof binomial coefficient

Published on 11 Apr 2026 - 4:08

score 64 · Answer 4 · 2026-04-12 13:48:09

64

Views

How can I prove this by mathematical induction

Published on 12 Apr 2026 - 13:48

score 113 · Answer 5 · 2026-04-17 11:39:02

113

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Is this proof valid? The claim is $2^{k} < (k+1)!$ for $k \geq 2$

Published on 17 Apr 2026 - 11:39

score 125 · Answer 6 · 2026-04-16 12:49:51

125

Views

Showing that $n! > n^2$ for $n\geq4$ by induction

Published on 16 Apr 2026 - 12:49

score 144 · Answer 7 · 2026-04-17 12:29:24

Showing $\frac{d^2}{dr^2}\left(\frac{1}{r}\frac{d}{dr}\right)^{k-1}(r^{2k-1}\phi(r))=\left(\frac{1}{r}\frac{d}{dr}\right)^{k}(r^{2k}\phi'(r))$

score 83 · Answer 8 · 2026-04-17 08:29:05

Use Complete Induction of set theory to prove $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... + \frac{1}{\sqrt{n}} > \sqrt{n}$.

score 305 · Answer 9 · 2026-04-10 17:43:27

305

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Induction proof for Fibonacci sum different notation

Published on 10 Apr 2026 - 17:43

score 154 · Answer 10 · 2026-04-14 18:09:55

154

Views

Prove that $\displaystyle \sum_{k=1}^n \bigg(\dfrac{1}{k}+\dfrac{2}{k+n}\bigg ) \leq \ln(2n) + 2 -\ln(2)$

Published on 14 Apr 2026 - 18:09

score 45 · Answer 11 · 2026-04-16 04:07:13

45

Views

Mathematical Induction to show positive real number other than 1

Published on 16 Apr 2026 - 4:07

score 76 · Answer 12 · 2026-04-17 00:38:17

76

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Request for a proof that $\sum\limits_{i=1}^n i^{k+1}=(n+1)\sum\limits_{i=1}^n i^k-\sum\limits_{p=1}^n\sum\limits_{i=1}^p i^k$

Published on 17 Apr 2026 - 0:38

score 129 · Answer 13 · 2026-04-14 13:35:29

129

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Prove by induction that $\sum_{k=0}^n k\cdot k! = (n+1)!-1$

Published on 14 Apr 2026 - 13:35

score 10.8k · Answer 14 · 2026-04-16 01:31:31

10.8k

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For all integers $n ≥ 2, n^3 > 2n + 1$

Published on 16 Apr 2026 - 1:31

score 24 · Answer 15 · 2026-04-13 18:41:44

24

Views

Correctness of use induction in the proof

Published on 13 Apr 2026 - 18:41

List Question

Given the recurrence $T_n = 2T_{n-1} - T_{n-2}$, prove by Induction that $T_n = n$

Mathematical induction proof problem: $\sum_{i=1}^{n-1} i(i+1) = \frac{n(n+1)(n-1)}3$

Proof binomial coefficient

How can I prove this by mathematical induction

Is this proof valid? The claim is $2^{k} < (k+1)!$ for $k \geq 2$

Showing that $n! > n^2$ for $n\geq4$ by induction

Showing $\frac{d^2}{dr^2}\left(\frac{1}{r}\frac{d}{dr}\right)^{k-1}(r^{2k-1}\phi(r))=\left(\frac{1}{r}\frac{d}{dr}\right)^{k}(r^{2k}\phi'(r))$

Use Complete Induction of set theory to prove $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... + \frac{1}{\sqrt{n}} > \sqrt{n}$.

Induction proof for Fibonacci sum different notation

Prove that $\displaystyle \sum_{k=1}^n \bigg(\dfrac{1}{k}+\dfrac{2}{k+n}\bigg ) \leq \ln(2n) + 2 -\ln(2)$

Mathematical Induction to show positive real number other than 1

Request for a proof that $\sum\limits_{i=1}^n i^{k+1}=(n+1)\sum\limits_{i=1}^n i^k-\sum\limits_{p=1}^n\sum\limits_{i=1}^p i^k$

Prove by induction that $\sum_{k=0}^n k\cdot k! = (n+1)!-1$

For all integers $n ≥ 2, n^3 > 2n + 1$

Correctness of use induction in the proof

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