Question

Finding $\lim{_{n \to \infty } } \frac{\frac{\sin(1)}{1}+\frac{\sin(2)}{2}+\frac{\sin(3)}{3}+...+\frac{\sin(n)}{n} }{n}$

score 149 · Answer 1 · 2026-04-17 03:59:31

149

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Finding $\lim{_{n \to \infty } } \frac{\frac{\sin(1)}{1}+\frac{\sin(2)}{2}+\frac{\sin(3)}{3}+...+\frac{\sin(n)}{n} }{n}$

Published on 17 Apr 2026 - 3:59

score 61 · Answer 2 · 2026-04-14 08:58:04

61

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Triple Summation Of Product Of Binomial Coefficients

Published on 14 Apr 2026 - 8:58

score 193 · Answer 3 · 2026-04-12 09:22:06

193

Views

Closed form for Compound Binomial Poisson PMF.

Published on 12 Apr 2026 - 9:22

score 227 · Answer 4 · 2026-04-17 09:49:57

227

Views

Prove that $\sum _{k=0}^n \left(\sum _{j=0}^k \binom{n}{j}\right)^3=\left(\frac{n}{2}+1\right) 8^n-\frac{3}{4} n 2^n \binom{2 n}{n}$

Published on 17 Apr 2026 - 9:49

score 557 · Answer 5 · 2026-04-13 09:40:27

557

Views

Proof that $\sum(\frac{(-1)^n}{\sqrt{n}} + \frac1n)$ diverges

Published on 13 Apr 2026 - 9:40

score 183 · Answer 6 · 2026-04-14 07:44:23

183

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The partial sum $\sum_{n \le N} \mu(n)/n \ne 0$ for finite $N \in \mathbb{N}$

Published on 14 Apr 2026 - 7:44

score 75 · Answer 7 · 2026-04-14 02:31:30

75

Views

Prove the following inequality with one integral and one sum

Published on 14 Apr 2026 - 2:31

score 33 · Answer 8 · 2026-04-16 15:26:52

33

Views

Why is $\sum_{j=1}^n (n-j+1) \ge \sum_{j=\lceil n/2 \rceil}^n (n/2) \ge n^2/4$?

Published on 16 Apr 2026 - 15:26

score 634 · Answer 9 · 2026-04-10 02:02:51

634

Views

Calculate sum of sum using Z transform

Published on 10 Apr 2026 - 2:02

score 52 · Answer 10 · 2026-04-09 19:41:03

52

Views

Can we define sum over an uncountable set?

Published on 09 Apr 2026 - 19:41

score 62 · Answer 11 · 2026-04-17 12:45:10

62

Views

Why $\sum_{x=y}^n 1 = n-y+1 ?$

Published on 17 Apr 2026 - 12:45

score 52 · Answer 12 · 2026-04-14 20:44:00

52

Views

Maximization Minimization Algorithm: Bradley-Terry Ranking

Published on 14 Apr 2026 - 20:44

score 231 · Answer 13 · 2026-04-15 11:57:49

231

Views

Does the sum $\frac{1}{3} + \frac{1}{3^{1+1/2}}+\cdots$ have a closed form?

Published on 15 Apr 2026 - 11:57

score 32 · Answer 14 · 2026-04-12 16:02:30

32

Views

Another Form For A Sum Of Geometric progression

Published on 12 Apr 2026 - 16:02

score 73 · Answer 15 · 2026-04-15 18:59:51

73

Views

Calculate $\sum_{i=2}^{∞} i\,\frac{\operatorname{fib}(i-1)}{2^i}$

Published on 15 Apr 2026 - 18:59

List Question

Finding $\lim{_{n \to \infty } } \frac{\frac{\sin(1)}{1}+\frac{\sin(2)}{2}+\frac{\sin(3)}{3}+...+\frac{\sin(n)}{n} }{n}$

Triple Summation Of Product Of Binomial Coefficients

Closed form for Compound Binomial Poisson PMF.

Prove that $\sum _{k=0}^n \left(\sum _{j=0}^k \binom{n}{j}\right)^3=\left(\frac{n}{2}+1\right) 8^n-\frac{3}{4} n 2^n \binom{2 n}{n}$

Proof that $\sum(\frac{(-1)^n}{\sqrt{n}} + \frac1n)$ diverges

The partial sum $\sum_{n \le N} \mu(n)/n \ne 0$ for finite $N \in \mathbb{N}$

Prove the following inequality with one integral and one sum

Why is $\sum_{j=1}^n (n-j+1) \ge \sum_{j=\lceil n/2 \rceil}^n (n/2) \ge n^2/4$?

Calculate sum of sum using Z transform

Can we define sum over an uncountable set?

Why $\sum_{x=y}^n 1 = n-y+1 ?$

Maximization Minimization Algorithm: Bradley-Terry Ranking

Does the sum $\frac{1}{3} + \frac{1}{3^{1+1/2}}+\cdots$ have a closed form?

Another Form For A Sum Of Geometric progression

Calculate $\sum_{i=2}^{∞} i\,\frac{\operatorname{fib}(i-1)}{2^i}$

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