Question

If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

score 219 · Answer 1 · 2026-05-11 09:36:21

219

Views

If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

Published on 11 May 2026 - 9:36

score 142 · Answer 2 · 2026-04-17 07:45:51

142

Views

Evaluate $\displaystyle \sum_{n=1}^{89}\tan^2\bigg(\frac{n\pi}{180}\bigg)$.

Published on 17 Apr 2026 - 7:45

score 1.9k · Answer 3 · 2026-05-11 05:33:27

1.9k

Views

If $\sum_{r=0}^{n-1}\log _2\left(\frac{r+2}{r+1}\right)= \prod_{r = 10}^{99}\log _r(r+1)$, then find $n$.

Published on 11 May 2026 - 5:33

score 22 · Answer 4 · 2026-04-16 15:06:37

22

Views

Find the top $k$ smallest sums above $N$ from the collection $S$ - Duplicates allowed

Published on 16 Apr 2026 - 15:06

score 67 · Answer 5 · 2026-05-02 01:04:54

67

Views

Is this formula true? $a + \sum_{n=1}^{\infty}a\left(\frac{x}{y}\right)^n = \frac{y}{y-x}a$

Published on 02 May 2026 - 1:04

score 54 · Answer 6 · 2026-04-13 07:25:33

54

Views

General formula for the number of terms from when evaluating the product of n terms $\Pi_{i=1}^{n}(1+x_i)^n$?

Published on 13 Apr 2026 - 7:25

score 1.6k · Answer 7 · 2026-04-13 11:51:35

1.6k

Views

Is it possible to justify these approximations about prime numbers?

Published on 13 Apr 2026 - 11:51

score 53 · Answer 8 · 2026-04-12 13:18:27

53

Views

Proving an equation involving a sum of inverted polynomials

Published on 12 Apr 2026 - 13:18

score 180 · Answer 9 · 2026-04-14 06:54:07

180

Views

Limit of Hypergeometric function

Published on 14 Apr 2026 - 6:54

score 82 · Answer 10 · 2026-04-12 12:30:09

82

Views

Equality between sums

Published on 12 Apr 2026 - 12:30

score 199 · Answer 11 · 2026-04-14 01:05:17

199

Views

How to show that $2\sum_{j=1}^{N}\cot(\frac{\pi j}{2N+1})$ is related to $(\frac{4 \text{N}+2}{\pi}) (H_{\text{N}}+\log (\frac{2}{\pi }))$?

Published on 14 Apr 2026 - 1:05

score 84 · Answer 12 · 2026-04-16 04:36:46

84

Views

Infinite sum $\sum ^{\infty }_{n=1}\frac {n( n+1)^{2}}{(n-1)!}x^{n}$

Published on 16 Apr 2026 - 4:36

score 142 · Answer 13 · 2026-04-07 19:48:13

142

Views

Convicted of squares in an Inequality and my Weakness

Published on 07 Apr 2026 - 19:48

score 102 · Answer 14 · 2026-04-17 07:36:25

102

Views

Combinatorial Argument (in Summation Notation)

Published on 17 Apr 2026 - 7:36

score 136 · Answer 15 · 2026-04-11 22:02:37

136

Views

Strange Cube Root Offense in an Inequality

Published on 11 Apr 2026 - 22:02

List Question

If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

Evaluate $\displaystyle \sum_{n=1}^{89}\tan^2\bigg(\frac{n\pi}{180}\bigg)$.

If $\sum_{r=0}^{n-1}\log _2\left(\frac{r+2}{r+1}\right)= \prod_{r = 10}^{99}\log _r(r+1)$, then find $n$.

Find the top $k$ smallest sums above $N$ from the collection $S$ - Duplicates allowed

Is this formula true? $a + \sum_{n=1}^{\infty}a\left(\frac{x}{y}\right)^n = \frac{y}{y-x}a$

General formula for the number of terms from when evaluating the product of n terms $\Pi_{i=1}^{n}(1+x_i)^n$?

Is it possible to justify these approximations about prime numbers?

Proving an equation involving a sum of inverted polynomials

Limit of Hypergeometric function

Equality between sums

How to show that $2\sum_{j=1}^{N}\cot(\frac{\pi j}{2N+1})$ is related to $(\frac{4 \text{N}+2}{\pi}) (H_{\text{N}}+\log (\frac{2}{\pi }))$?

Infinite sum $\sum ^{\infty }_{n=1}\frac {n( n+1)^{2}}{(n-1)!}x^{n}$

Convicted of squares in an Inequality and my Weakness

Combinatorial Argument (in Summation Notation)

Strange Cube Root Offense in an Inequality

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