Question

Show, with induction that $1^2 + 2^2 + .... + n^2 = \frac{n(n+1)(2n+1)}{6}$

score 88 · Answer 1 · 2019-04-15 19:03:46

Show, with induction that $1^2 + 2^2 + .... + n^2 = \frac{n(n+1)(2n+1)}{6}$

Published on 15 Apr 2019 - 19:03

score 50 · Answer 2 · 2026-03-25 09:30:00

Show that if $x_{0}=1$ and $x_{n+1}=1+\frac{1}{x_n}$ then $|\varphi-x_n|\leq \frac{1}{\varphi^{n+1}}$ and $x_n\rightarrow \varphi$

score 140 · Answer 3 · 2026-03-31 22:47:54

140

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Prove the statement, For all integers $n ≥ 0$, $y_n = 3 * 2^n + 4^n$ where $y_0 = 4, y_1 = 10$ and when $n ≥ 2$, $y_n = 6y_{n-1} – 8y_{n-2} $

Published on 31 Mar 2026 - 22:47

score 123 · Answer 4 · 2026-03-29 21:23:19

123

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Proof - Graph Connectedness

Published on 29 Mar 2026 - 21:23

score 49 · Answer 5 · 2019-04-16 21:16:14

49

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Show with that induction $\sum_{k=0}^{n} 2{^{2k}}=\frac{2^{2n+2}-1}{3}$, for n = 0,1,2...

Published on 16 Apr 2019 - 21:16

score 234 · Answer 6 · 2019-04-17 16:50:32

234

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Demonstration by induction without using the induction hypothesis

Published on 17 Apr 2019 - 16:50

score 94 · Answer 7 · 2019-04-17 17:53:13

94

Views

Show with induction that $\sum_{k=1}^{n} \frac{k^{2}}{2^{k}} = 6 - \frac{n^2+4n+6}{2^{n}}$

Published on 17 Apr 2019 - 17:53

score 48 · Answer 8 · 2019-04-18 10:34:03

48

Views

Show that $\sum_{k=1}^{n}(5^{2k}-5^{2k-1})=\frac{5^{2n+1}-5}{6}$, for n = 1,2,3, ...

Published on 18 Apr 2019 - 10:34

score 185 · Answer 9 · 2019-04-18 14:52:17

185

Views

Prove that if $n \in \omega$ then $n \notin n$

Published on 18 Apr 2019 - 14:52

score 35 · Answer 10 · 2019-04-19 04:20:32

35

Views

prove by induction that 2^n/n! < 4/n

Published on 19 Apr 2019 - 4:20

score 560 · Answer 11 · 2019-04-19 18:22:51

560

Views

Induction Proof for Sequences

Published on 19 Apr 2019 - 18:22

score 77 · Answer 12 · 2019-04-19 20:20:14

77

Views

I need help with induction proof

Published on 19 Apr 2019 - 20:20

score 137 · Answer 13 · 2026-03-26 02:47:38

137

Views

Induction Proof: Define the sequence $ \ \ T_1, T_2, T_3,...\ \ $ by $\ \ T_1=T_2=T_3=1 \ \ $ and $ \ \ T_{k+1}= T_{k}+T_{k-1}+T_{k-2}$.

Published on 26 Mar 2026 - 2:47

score 6.3k · Answer 14 · 2019-04-19 22:13:16

6.3k

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Proof that an even number plus an odd number is equals to an odd number

Published on 19 Apr 2019 - 22:13

score 211 · Answer 15 · 2026-03-25 22:09:52

211

Views

fibonacci and lucas numbers induction

Published on 25 Mar 2026 - 22:09

List Question

Show, with induction that $1^2 + 2^2 + .... + n^2 = \frac{n(n+1)(2n+1)}{6}$

Show that if $x_{0}=1$ and $x_{n+1}=1+\frac{1}{x_n}$ then $|\varphi-x_n|\leq \frac{1}{\varphi^{n+1}}$ and $x_n\rightarrow \varphi$

Prove the statement, For all integers $n ≥ 0$, $y_n = 3 * 2^n + 4^n$ where $y_0 = 4, y_1 = 10$ and when $n ≥ 2$, $y_n = 6y_{n-1} – 8y_{n-2} $

Proof - Graph Connectedness

Show with that induction $\sum_{k=0}^{n} 2{^{2k}}=\frac{2^{2n+2}-1}{3}$, for n = 0,1,2...

Demonstration by induction without using the induction hypothesis

Show with induction that $\sum_{k=1}^{n} \frac{k^{2}}{2^{k}} = 6 - \frac{n^2+4n+6}{2^{n}}$

Show that $\sum_{k=1}^{n}(5^{2k}-5^{2k-1})=\frac{5^{2n+1}-5}{6}$, for n = 1,2,3, ...

Prove that if $n \in \omega$ then $n \notin n$

prove by induction that 2^n/n! < 4/n

Induction Proof for Sequences

I need help with induction proof

Induction Proof: Define the sequence $ \ \ T_1, T_2, T_3,...\ \ $ by $\ \ T_1=T_2=T_3=1 \ \ $ and $ \ \ T_{k+1}= T_{k}+T_{k-1}+T_{k-2}$.

Proof that an even number plus an odd number is equals to an odd number

fibonacci and lucas numbers induction

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