Question

Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$

score 2.8k · Answer 1 · 2026-04-16 17:14:05

2.8k

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Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$

Published on 16 Apr 2026 - 17:14

score 1.5k · Answer 2 · 2026-04-15 06:39:18

1.5k

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prove that the greatest number of regions that $n \geq 1$ circles can divide the plane is $n^2-n+2$

Published on 15 Apr 2026 - 6:39

score 2.8k · Answer 3 · 2026-04-14 01:19:37

2.8k

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There are no bearded men in the world - What goes wrong in this proof?

Published on 14 Apr 2026 - 1:19

score 777 · Answer 4 · 2026-04-14 00:37:33

777

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Proving property of Legendre Polynomial (by induction?)

Published on 14 Apr 2026 - 0:37

score 776 · Answer 5 · 2026-04-16 07:34:54

776

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In the marriage problem, if each girl knows at least $m$ boys, then there are at least $m!$ ways to arrange the marriages.

Published on 16 Apr 2026 - 7:34

score 238 · Answer 6 · 2026-04-14 22:31:56

238

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If $J$ is the $n×n$ matrix of all ones, and $A = (l−b)I +bJ$, then $\det(A) = (l − b)^{n−1}(l + (n − 1)b)$

Published on 14 Apr 2026 - 22:31

score 339 · Answer 7 · 2026-04-12 18:41:59

339

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"If $n=0$ there is nothing to prove"

Published on 12 Apr 2026 - 18:41

score 2.5k · Answer 8 · 2026-04-11 01:39:18

2.5k

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Mathematical Induction: how do we know what applies to one thing also applies to another?

Published on 11 Apr 2026 - 1:39

score 4.5k · Answer 9 · 2026-04-12 07:45:57

4.5k

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Using induction, prove that every forest is a bipartite graph

Published on 12 Apr 2026 - 7:45

score 562 · Answer 10 · 2026-05-14 19:02:29

562

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Induction hypothesis when proving solution to linear homogeneous recurrence equation

Published on 14 May 2026 - 19:02

score 831 · Answer 11 · 2026-04-13 13:34:27

831

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Formal definition of Mathematical Induction & Strong Induction

Published on 13 Apr 2026 - 13:34

score 105 · Answer 12 · 2026-04-17 04:35:03

105

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Proving $r_0+r_1a+r_2a^2+\cdots+r_{k-1}a^{k-1} < a^k$ by INDUCTION.

Published on 17 Apr 2026 - 4:35

score 123 · Answer 13 · 2026-04-14 17:14:36

123

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Check proof by induction of $\sum_{i=0}^n i^4 = \frac15 n^5+\frac12n^4+\frac13n^3-\frac1{30}n $

Published on 14 Apr 2026 - 17:14

score 114 · Answer 14 · 2026-04-11 03:20:17

114

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Mathematical Induction (power of four exceeds multiple of three by one)

Published on 11 Apr 2026 - 3:20

score 664 · Answer 15 · 2026-04-16 08:34:24

664

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Induction proof of $\sum_{j=0}^n{(-1)^j{n \choose j}\prod_{k=m+1}^{m+n-1}{(j+k)}}=0$

Published on 16 Apr 2026 - 8:34

List Question

Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$

prove that the greatest number of regions that $n \geq 1$ circles can divide the plane is $n^2-n+2$

There are no bearded men in the world - What goes wrong in this proof?

Proving property of Legendre Polynomial (by induction?)

In the marriage problem, if each girl knows at least $m$ boys, then there are at least $m!$ ways to arrange the marriages.

If $J$ is the $n×n$ matrix of all ones, and $A = (l−b)I +bJ$, then $\det(A) = (l − b)^{n−1}(l + (n − 1)b)$

"If $n=0$ there is nothing to prove"

Mathematical Induction: how do we know what applies to one thing also applies to another?

Using induction, prove that every forest is a bipartite graph

Induction hypothesis when proving solution to linear homogeneous recurrence equation

Formal definition of Mathematical Induction & Strong Induction

Proving $r_0+r_1a+r_2a^2+\cdots+r_{k-1}a^{k-1} < a^k$ by INDUCTION.

Check proof by induction of $\sum_{i=0}^n i^4 = \frac15 n^5+\frac12n^4+\frac13n^3-\frac1{30}n $

Mathematical Induction (power of four exceeds multiple of three by one)

Induction proof of $\sum_{j=0}^n{(-1)^j{n \choose j}\prod_{k=m+1}^{m+n-1}{(j+k)}}=0$

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