Question

Prove using congruences that $ 7\mid\left(5^{2n}+3\cdot 2^{5n-2}\right)$ , $n \ge 1$

score 5.4k · Answer 1 · 2026-04-15 21:16:13

5.4k

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Prove using congruences that $ 7\mid\left(5^{2n}+3\cdot 2^{5n-2}\right)$ , $n \ge 1$

Published on 15 Apr 2026 - 21:16

score 626 · Answer 2 · 2026-04-15 23:24:47

626

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Prove $ \sum_{k=0}^n k4^k = \frac 49((3n-1)4^n + 1) $ by induction

Published on 15 Apr 2026 - 23:24

score 88 · Answer 3 · 2026-04-13 19:23:21

88

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Mathematical induction with two nested sums

Published on 13 Apr 2026 - 19:23

score 610 · Answer 4 · 2026-04-15 20:21:14

610

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Prove that $\frac {(2n)!} {(n!)^2} > \frac{4^n}{n + 1} $

Published on 15 Apr 2026 - 20:21

score 4k · Answer 5 · 2026-04-14 19:26:18

4k

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Induction: Every connected graph has a spanning tree

Published on 14 Apr 2026 - 19:26

score 15.6k · Answer 6 · 2026-04-16 07:27:35

Prove by induction $ \sin x + \sin 2x + ... + \sin nx = \frac {\sin (\frac {n + 1} {2} x)} {\sin \frac{x}{2}} \sin \frac{nx}{2} $

score 58 · Answer 7 · 2026-04-11 15:17:48

58

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which is the best proof to use for gcd(a, b) = gcd(a, b − a)

Published on 11 Apr 2026 - 15:17

score 1.8k · Answer 8 · 2026-04-18 15:07:19

1.8k

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proving that if $x^2 + x + 1$ is even, then $x$ is odd by induction

Published on 18 Apr 2026 - 15:07

score 112 · Answer 9 · 2015-11-21 04:41:54

112

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The sum of binomial coefficients $\sum_{i=1}^n \binom{i}{2}= {n+1 \choose 3}$

Published on 21 Nov 2015 - 4:41

score 55 · Answer 10 · 2026-04-08 20:02:30

55

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Induction on powers

Published on 08 Apr 2026 - 20:02

score 80 · Answer 11 · 2026-04-12 00:42:13

80

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Prove $\frac n2 > \sum_{k=1}^n (1/k) -1$

Published on 12 Apr 2026 - 0:42

score 57 · Answer 12 · 2026-03-29 10:59:03

57

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A recursive definition

Published on 29 Mar 2026 - 10:59

score 82 · Answer 13 · 2026-04-16 00:23:56

82

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A possible error in the inductive proof of $2k+1<2^k$ for $k\ge 3$

Published on 16 Apr 2026 - 0:23

score 71 · Answer 14 · 2026-04-16 06:21:49

71

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Prove with induction that $a_n = 2^n-1$

Published on 16 Apr 2026 - 6:21

score 184 · Answer 15 · 2026-04-09 18:01:19

184

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Is induction defined on natural numbers?

Published on 09 Apr 2026 - 18:01

List Question

Prove using congruences that $ 7\mid\left(5^{2n}+3\cdot 2^{5n-2}\right)$ , $n \ge 1$

Prove $ \sum_{k=0}^n k4^k = \frac 49((3n-1)4^n + 1) $ by induction

Mathematical induction with two nested sums

Prove that $\frac {(2n)!} {(n!)^2} > \frac{4^n}{n + 1} $

Induction: Every connected graph has a spanning tree

Prove by induction $ \sin x + \sin 2x + ... + \sin nx = \frac {\sin (\frac {n + 1} {2} x)} {\sin \frac{x}{2}} \sin \frac{nx}{2} $

which is the best proof to use for gcd(a, b) = gcd(a, b − a)

proving that if $x^2 + x + 1$ is even, then $x$ is odd by induction

The sum of binomial coefficients $\sum_{i=1}^n \binom{i}{2}= {n+1 \choose 3}$

Induction on powers

Prove $\frac n2 > \sum_{k=1}^n (1/k) -1$

A recursive definition

A possible error in the inductive proof of $2k+1<2^k$ for $k\ge 3$

Prove with induction that $a_n = 2^n-1$

Is induction defined on natural numbers?

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