Question

prove using strong mathematical induction $S_{k}=2^{((k+1)/2)}$

score 73 · Answer 1 · 2018-04-13 20:37:11

73

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prove using strong mathematical induction $S_{k}=2^{((k+1)/2)}$

Published on 13 Apr 2018 - 20:37

score 192 · Answer 2 · 2018-04-14 04:49:39

192

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How does Tom Apostol deduce the inequality $\frac{k^3}{3} + k^2 \lt \frac{(k + 1)^3}{3}$ in section I 1.3 of his proof by induction example?

Published on 14 Apr 2018 - 4:49

score 116 · Answer 3 · 2018-04-14 20:13:38

116

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Suppose $(a)_{j=1}^{\infty}$ is a sequence of real numbers. prove by induction on n that $|\sum_{j=1}^{n}a_j|\leq\sum_{j=1}^{n}|a_j|$

Published on 14 Apr 2018 - 20:13

score 492 · Answer 4 · 2018-04-14 23:15:57

492

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How do I find the cardinality of strings in this set?

Published on 14 Apr 2018 - 23:15

score 8.3k · Answer 5 · 2026-03-25 07:31:12

8.3k

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The "assumption" in proof by induction

Published on 25 Mar 2026 - 7:31

score 37 · Answer 6 · 2018-04-15 11:31:07

37

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How do I figure out which side is easier to manipulate?

Published on 15 Apr 2018 - 11:31

score 122 · Answer 7 · 2018-04-15 13:28:16

122

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Proving an Inequality in Fourier Transformation

Published on 15 Apr 2018 - 13:28

score 67 · Answer 8 · 2026-03-25 13:04:59

67

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Proving that ${4a \choose 2a} - {2a \choose a}$ is divisible by 4

Published on 25 Mar 2026 - 13:04

score 1.8k · Answer 9 · 2018-04-16 01:49:51

1.8k

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Formula for $\sum_{k=1}^n k2^k$

Published on 16 Apr 2018 - 1:49

score 145 · Answer 10 · 2018-04-16 03:56:53

145

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Prove for every natural number $n$, with $n ≥ 7$, that $\frac{(2n−18)}{(n^2−8n+ 8)} < 1$.

Published on 16 Apr 2018 - 3:56

score 33 · Answer 11 · 2026-03-25 06:05:55

33

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Connectedness, Products of Finite Topologies

Published on 25 Mar 2026 - 6:05

score 90 · Answer 12 · 2018-04-16 08:16:38

90

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Prove by induction: $b_n=\frac{n^n}{n!}$, where $b_1 = 1$ and $b_{n+1} = \left(1+\frac{1}{n}\right)^n\times b_n$

Published on 16 Apr 2018 - 8:16

score 268 · Answer 13 · 2026-03-25 03:42:25

268

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Proof by induction for $\left(1−\frac14\right)\cdot\left(1−\frac19\right)\cdots\left(1−\frac1{n^2}\right)$ for all natural numbers $n$ with $n \ge 2$

Published on 25 Mar 2026 - 3:42

score 1k · Answer 14 · 2026-03-25 12:52:31

1k

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Predicate logic statements with one and multi parameters

Published on 25 Mar 2026 - 12:52

score 123 · Answer 15 · 2026-03-25 06:21:06

123

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Regular languages: Prove $2^n + n < 2^{n+1}$ for $n \ge 1$

Published on 25 Mar 2026 - 6:21

List Question

prove using strong mathematical induction $S_{k}=2^{((k+1)/2)}$

How does Tom Apostol deduce the inequality $\frac{k^3}{3} + k^2 \lt \frac{(k + 1)^3}{3}$ in section I 1.3 of his proof by induction example?

Suppose $(a)_{j=1}^{\infty}$ is a sequence of real numbers. prove by induction on n that $|\sum_{j=1}^{n}a_j|\leq\sum_{j=1}^{n}|a_j|$

How do I find the cardinality of strings in this set?

The "assumption" in proof by induction

How do I figure out which side is easier to manipulate?

Proving an Inequality in Fourier Transformation

Proving that ${4a \choose 2a} - {2a \choose a}$ is divisible by 4

Formula for $\sum_{k=1}^n k2^k$

Prove for every natural number $n$, with $n ≥ 7$, that $\frac{(2n−18)}{(n^2−8n+ 8)} < 1$.

Connectedness, Products of Finite Topologies

Prove by induction: $b_n=\frac{n^n}{n!}$, where $b_1 = 1$ and $b_{n+1} = \left(1+\frac{1}{n}\right)^n\times b_n$

Proof by induction for $\left(1−\frac14\right)\cdot\left(1−\frac19\right)\cdots\left(1−\frac1{n^2}\right)$ for all natural numbers $n$ with $n \ge 2$

Predicate logic statements with one and multi parameters

Regular languages: Prove $2^n + n < 2^{n+1}$ for $n \ge 1$

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