Question

Show that 3^(n-1) is greater than or equal to n^2 by mathematical induction

score 46 · Answer 1 · 2020-05-06 14:50:38

46

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Show that 3^(n-1) is greater than or equal to n^2 by mathematical induction

Published on 06 May 2020 - 14:50

score 41 · Answer 2 · 2020-05-06 16:38:19

41

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Prove by induction $1+2+2^{2}+...+2^{n-1} =2^{n}-1; \forall n \geqslant 1$

Published on 06 May 2020 - 16:38

score 27 · Answer 3 · 2026-04-11 05:59:50

27

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What is the correct statement for $n\in N$

Published on 11 Apr 2026 - 5:59

score 913 · Answer 4 · 2020-05-06 18:04:32

Let $P(n)$ be a statement and let $P(n) \rightarrow P(n+1)$ is true for natural numbers n, the $P(n)$ is true for

score 80 · Answer 5 · 2020-05-06 23:19:25

80

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Prove by Mathematical Induction that $3^n > n^2 + 4$ for $n\geq 2$.

Published on 06 May 2020 - 23:19

score 73 · Answer 6 · 2020-05-07 03:08:00

73

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Show $\sum_{k = 1}^n (k+1)2^k = n2^{n+1}$ by mathematical induction.

Published on 07 May 2020 - 3:08

score 80 · Answer 7 · 2020-05-07 06:11:54

80

Views

Let $m\in N$ with $m\geq 2$. Then for all $n\in N$: $m^n> n$.

Published on 07 May 2020 - 6:11

score 123 · Answer 8 · 2020-05-07 11:50:55

123

Views

Prove that: $1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2n+1}$ is not an Integer for any integer $n$

Published on 07 May 2020 - 11:50

score 168 · Answer 9 · 2020-05-07 14:47:28

168

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How to prove that $\ln (N+1) - \ln (N) \geq \frac{1}{N+1}$

Published on 07 May 2020 - 14:47

score 64 · Answer 10 · 2020-05-07 21:13:54

Prove that for all $n\in \mathbb{N}$, it holds that for all real numbers $a,b\geq 0$, that $(\frac{a+b}{2})^n \leq \frac{a^n+b^n}{2}$

score 73 · Answer 11 · 2026-03-30 08:17:58

73

Views

Correctness with/without induction

Published on 30 Mar 2026 - 8:17

score 93 · Answer 12 · 2026-03-28 21:51:45

93

Views

$ \vert x_m - x_n\vert \le \frac{K^{n-1}}{1-K}\vert x_2-x_1\vert $

Published on 28 Mar 2026 - 21:51

score 58 · Answer 13 · 2020-05-08 18:59:32

58

Views

Sequences with strong inductional proof

Published on 08 May 2020 - 18:59

score 224 · Answer 14 · 2020-05-09 05:52:45

224

Views

Proving for any nonnegative integer $k$, $[T^k]_\beta=([T]_\beta)^k.$

Published on 09 May 2020 - 5:52

score 113 · Answer 15 · 2020-05-09 14:37:24

113

Views

Prove by Induction - Modular arithmetic with Logarithms

Published on 09 May 2020 - 14:37

List Question

Show that 3^(n-1) is greater than or equal to n^2 by mathematical induction

Prove by induction $1+2+2^{2}+...+2^{n-1} =2^{n}-1; \forall n \geqslant 1$

What is the correct statement for $n\in N$

Let $P(n)$ be a statement and let $P(n) \rightarrow P(n+1)$ is true for natural numbers n, the $P(n)$ is true for

Prove by Mathematical Induction that $3^n > n^2 + 4$ for $n\geq 2$.

Show $\sum_{k = 1}^n (k+1)2^k = n2^{n+1}$ by mathematical induction.

Let $m\in N$ with $m\geq 2$. Then for all $n\in N$: $m^n> n$.

Prove that: $1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2n+1}$ is not an Integer for any integer $n$

How to prove that $\ln (N+1) - \ln (N) \geq \frac{1}{N+1}$

Prove that for all $n\in \mathbb{N}$, it holds that for all real numbers $a,b\geq 0$, that $(\frac{a+b}{2})^n \leq \frac{a^n+b^n}{2}$

Correctness with/without induction

$ \vert x_m - x_n\vert \le \frac{K^{n-1}}{1-K}\vert x_2-x_1\vert $

Sequences with strong inductional proof

Proving for any nonnegative integer $k$, $[T^k]_\beta=([T]_\beta)^k.$

Prove by Induction - Modular arithmetic with Logarithms

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