Question

prove: $\lim\limits_{t \to 0} (\frac{1}{n}\sum_{k=1}^{n}x_{k}^{t})^{\frac{1}{t}} = (x_{1}\cdots x_{n})^{\frac{1}{n}} $

score 51 · Answer 1 · 2026-04-16 15:58:41

51

Views

prove: $\lim\limits_{t \to 0} (\frac{1}{n}\sum_{k=1}^{n}x_{k}^{t})^{\frac{1}{t}} = (x_{1}\cdots x_{n})^{\frac{1}{n}} $

Published on 16 Apr 2026 - 15:58

score 64 · Answer 2 · 2026-04-16 16:29:45

64

Views

For any prime $p>3$ show that $C_{np}^{p}-C_{np}^{2p}+C_{np}^{3p}-C_{np}^{4p}+...+(-1)^{n-1}C_{np}^{np} \equiv 1\pmod{p^3}$

Published on 16 Apr 2026 - 16:29

score 58 · Answer 3 · 2026-04-08 19:58:08

58

Views

How to simlpify this Sum?

Published on 08 Apr 2026 - 19:58

score 45 · Answer 4 · 2026-04-14 17:14:25

45

Views

Indexed summation and product

Published on 14 Apr 2026 - 17:14

score 89 · Answer 5 · 2026-04-16 23:23:25

89

Views

Evaluate: $\sum_{k=0}^{n}(-4)^k\frac{{n+k \choose 2k}}{ak+b}$

Published on 16 Apr 2026 - 23:23

score 26 · Answer 6 · 2026-04-11 08:39:36

26

Views

Is the product of two vectors of null sum, a vector with null sum?

Published on 11 Apr 2026 - 8:39

score 77 · Answer 7 · 2026-04-16 07:38:04

77

Views

Calculate the sum $\sum_{n=1}^{\infty}\Big((2n-1)\Big(\sum_{k=n}^{\infty}\frac{1}{k^2}\Big)-2\Big) $

Published on 16 Apr 2026 - 7:38

score 36 · Answer 8 · 2026-03-25 09:31:38

36

Views

How do I evaluate this summation series?

Published on 25 Mar 2026 - 9:31

score 27 · Answer 9 · 2026-04-13 10:14:08

27

Views

A legal reordering of two sigma notations

Published on 13 Apr 2026 - 10:14

score 207 · Answer 10 · 2026-04-16 20:07:58

207

Views

sum over combination of binomial coefficients similar to Vandermonde identity, but with extra power series factor

Published on 16 Apr 2026 - 20:07

score 78 · Answer 11 · 2026-04-11 12:05:30

78

Views

Geometric inequality in triangle with inradius

Published on 11 Apr 2026 - 12:05

score 67 · Answer 12 · 2026-04-10 12:01:06

67

Views

proof problem of combination and summation

Published on 10 Apr 2026 - 12:01

score 230 · Answer 13 · 2026-04-08 21:47:23

230

Views

Average of function defined on cantor set

Published on 08 Apr 2026 - 21:47

score 350 · Answer 14 · 2026-04-16 03:16:06

350

Views

How to find range $a_{75}$ of the term of the series $a_n=a_{n-1}+ {1 \over {a_{n-1}}} $

Published on 16 Apr 2026 - 3:16

score 41 · Answer 15 · 2026-04-17 22:51:01

41

Views

Combinatorics question - $\sum_{k=0}^\infty \binom{a+k-1}{k}r^k$

Published on 17 Apr 2026 - 22:51

List Question

prove: $\lim\limits_{t \to 0} (\frac{1}{n}\sum_{k=1}^{n}x_{k}^{t})^{\frac{1}{t}} = (x_{1}\cdots x_{n})^{\frac{1}{n}} $

For any prime $p>3$ show that $C_{np}^{p}-C_{np}^{2p}+C_{np}^{3p}-C_{np}^{4p}+...+(-1)^{n-1}C_{np}^{np} \equiv 1\pmod{p^3}$

How to simlpify this Sum?

Indexed summation and product

Evaluate: $\sum_{k=0}^{n}(-4)^k\frac{{n+k \choose 2k}}{ak+b}$

Is the product of two vectors of null sum, a vector with null sum?

Calculate the sum $\sum_{n=1}^{\infty}\Big((2n-1)\Big(\sum_{k=n}^{\infty}\frac{1}{k^2}\Big)-2\Big) $

How do I evaluate this summation series?

A legal reordering of two sigma notations

sum over combination of binomial coefficients similar to Vandermonde identity, but with extra power series factor

Geometric inequality in triangle with inradius

proof problem of combination and summation

Average of function defined on cantor set

How to find range $a_{75}$ of the term of the series $a_n=a_{n-1}+ {1 \over {a_{n-1}}} $

Combinatorics question - $\sum_{k=0}^\infty \binom{a+k-1}{k}r^k$

Trending Questions

Popular # Hahtags

Popular Questions