Question

Prove $(1 - a)^n \geq 1 - na$ for $0 < a < 1$

score 5k · Answer 1 · 2014-03-13 16:42:22

5k

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Prove $(1 - a)^n \geq 1 - na$ for $0 < a < 1$

Published on 13 Mar 2014 - 16:42

score 158 · Answer 2 · 2014-03-13 16:58:12

158

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prove combinatorical identity using induction

Published on 13 Mar 2014 - 16:58

score 295 · Answer 3 · 2014-03-14 08:56:33

295

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Mathematical Induction proof that $\sum\limits_{i=1}^n \frac{1}{i^2} < 2 - \frac1n$

Published on 14 Mar 2014 - 8:56

score 124 · Answer 4 · 2014-03-14 20:09:59

124

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Understanding math behind proof relating to binary search trees (issue with logarithms)

Published on 14 Mar 2014 - 20:09

score 311 · Answer 5 · 2014-03-15 00:27:40

311

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Prove by induction that $\sum_{i=0}^n \left(\frac 3 2 \right)^i = 2\left(\frac 3 2 \right)^{n+1} -2$

Published on 15 Mar 2014 - 0:27

score 310 · Answer 6 · 2014-03-15 09:38:14

310

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Induction proof of $n^{(n+1) }> n(n+1)^{(n-1)}$

Published on 15 Mar 2014 - 9:38

score 1k · Answer 7 · 2026-04-01 18:47:17

1k

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[Beginner]How to tackle mathematical proofs?

Published on 01 Apr 2026 - 18:47

score 70 · Answer 8 · 2014-03-16 10:01:40

70

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Taylor series like polynomials

Published on 16 Mar 2014 - 10:01

score 265 · Answer 9 · 2026-03-30 08:57:03

265

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Using induction to prove $\sum\limits^n_{k=1} 9^k = 0.5 \cdot \sum\limits^{2n}_{k=1} (-1)^k \cdot 3^{k+1}$

Published on 30 Mar 2026 - 8:57

score 280 · Answer 10 · 2014-03-18 01:30:37

280

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Proof that $\binom{ n}{k} \in \mathbb N$

Published on 18 Mar 2014 - 1:30

score 136 · Answer 11 · 2014-03-18 07:29:40

136

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Induction for a sequence starting with a negative and ending with a positive number.

Published on 18 Mar 2014 - 7:29

score 313 · Answer 12 · 2026-03-29 21:53:08

313

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Proving divisibility by using induction: $133 \mid (11^{n+2} + 12^{2n+1})$

Published on 29 Mar 2026 - 21:53

score 635 · Answer 13 · 2014-03-19 21:03:07

635

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Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$

Published on 19 Mar 2014 - 21:03

score 674 · Answer 14 · 2014-03-20 01:44:04

674

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Proof by induction of the value of $3^n$ modulo 10

Published on 20 Mar 2014 - 1:44

score 317 · Answer 15 · 2014-03-20 02:23:06

317

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How can I prove $2^n > n^2 $ by induction using a basis $> 4$

Published on 20 Mar 2014 - 2:23

List Question

Prove $(1 - a)^n \geq 1 - na$ for $0 < a < 1$

prove combinatorical identity using induction

Mathematical Induction proof that $\sum\limits_{i=1}^n \frac{1}{i^2} < 2 - \frac1n$

Understanding math behind proof relating to binary search trees (issue with logarithms)

Prove by induction that $\sum_{i=0}^n \left(\frac 3 2 \right)^i = 2\left(\frac 3 2 \right)^{n+1} -2$

Induction proof of $n^{(n+1) }> n(n+1)^{(n-1)}$

[Beginner]How to tackle mathematical proofs?

Taylor series like polynomials

Using induction to prove $\sum\limits^n_{k=1} 9^k = 0.5 \cdot \sum\limits^{2n}_{k=1} (-1)^k \cdot 3^{k+1}$

Proof that $\binom{ n}{k} \in \mathbb N$

Induction for a sequence starting with a negative and ending with a positive number.

Proving divisibility by using induction: $133 \mid (11^{n+2} + 12^{2n+1})$

Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$

Proof by induction of the value of $3^n$ modulo 10

How can I prove $2^n > n^2 $ by induction using a basis $> 4$

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