Question

Need to prove that $A_k=(-1)^k {n \choose k}$

score 34 · Answer 1 · 2017-04-13 20:37:45

34

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Need to prove that $A_k=(-1)^k {n \choose k}$

Published on 13 Apr 2017 - 20:37

score 105 · Answer 2 · 2017-04-14 08:58:40

105

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What is the positive integer number $n$ satisfying $(2n)!=n!\times(n+1)!$

Published on 14 Apr 2017 - 8:58

score 647 · Answer 3 · 2017-04-16 03:13:44

647

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$x$ and $y$ are natural numbers $x+y+21=3xy$. Find maximum possible integral power of $6$ in $(xy)$!

Published on 16 Apr 2017 - 3:13

score 14.4k · Answer 4 · 2017-04-16 09:39:00

14.4k

Views

What is the limit of the sequence n!/4^n?

Published on 16 Apr 2017 - 9:39

score 52 · Answer 5 · 2017-04-16 15:11:54

52

Views

Find the limit $\lim_{n\to \infty}\{{n!}^{1/n}\}/n$

Published on 16 Apr 2017 - 15:11

score 611 · Answer 6 · 2017-04-17 22:31:56

611

Views

Why does $\lim\limits_{x\to\infty}(x!)^{1/x}\neq 1?$

Published on 17 Apr 2017 - 22:31

score 287 · Answer 7 · 2017-04-18 02:00:10

287

Views

Simplification of factorials

Published on 18 Apr 2017 - 2:00

score 93 · Answer 8 · 2017-04-18 11:51:34

93

Views

Ways to prove $\sum_{A_k}^n \sum_{A_{k-1}}^{A_k} \sum_{A_{k-2}}^{A_{k-1}} \cdots \sum_{A_1}^{A_2} A_1 = {n+k \choose k+1}$

Published on 18 Apr 2017 - 11:51

score 430 · Answer 9 · 2017-04-18 15:32:33

430

Views

Determine $\sum\limits_{n=1}^{\infty }\frac{1}{(n!)!}$ conv or div?

Published on 18 Apr 2017 - 15:32

score 4.1k · Answer 10 · 2017-04-18 15:35:15

4.1k

Views

Mathematical Induction with factorial

Published on 18 Apr 2017 - 15:35

score 352 · Answer 11 · 2017-04-19 09:30:47

352

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How to determine whether a number can be expressed as a sum of factorials

Published on 19 Apr 2017 - 9:30

score 37 · Answer 12 · 2017-04-20 02:02:48

37

Views

Largest power of prime dividing n

Published on 20 Apr 2017 - 2:02

score 210 · Answer 13 · 2017-04-20 04:26:34

210

Views

Last $3$ digits of addition, Olympiad problem.

Published on 20 Apr 2017 - 4:26

score 66 · Answer 14 · 2026-04-02 03:48:33

66

Views

Is the equation $x^3-y^3\equiv k \mod n$ always solveable, when neither $7$ nor $9$ divides $n$?

Published on 02 Apr 2026 - 3:48

score 65 · Answer 15 · 2017-04-24 20:15:42

65

Views

$\frac{n!}{(n+\frac{1}{x})!} = ?$ for some positive real $x$

Published on 24 Apr 2017 - 20:15

List Question

Need to prove that $A_k=(-1)^k {n \choose k}$

What is the positive integer number $n$ satisfying $(2n)!=n!\times(n+1)!$

$x$ and $y$ are natural numbers $x+y+21=3xy$. Find maximum possible integral power of $6$ in $(xy)$!

What is the limit of the sequence n!/4^n?

Find the limit $\lim_{n\to \infty}\{{n!}^{1/n}\}/n$

Why does $\lim\limits_{x\to\infty}(x!)^{1/x}\neq 1?$

Simplification of factorials

Ways to prove $\sum_{A_k}^n \sum_{A_{k-1}}^{A_k} \sum_{A_{k-2}}^{A_{k-1}} \cdots \sum_{A_1}^{A_2} A_1 = {n+k \choose k+1}$

Determine $\sum\limits_{n=1}^{\infty }\frac{1}{(n!)!}$ conv or div?

Mathematical Induction with factorial

How to determine whether a number can be expressed as a sum of factorials

Largest power of prime dividing n

Last $3$ digits of addition, Olympiad problem.

Is the equation $x^3-y^3\equiv k \mod n$ always solveable, when neither $7$ nor $9$ divides $n$?

$\frac{n!}{(n+\frac{1}{x})!} = ?$ for some positive real $x$

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