Question

Evaluate: $\sum_{n=1}^{10}n\cdot (\sum_{r=1}^{10}\frac{r^2}{r+n})$

score 40 · Answer 1 · 2026-04-16 07:14:41

40

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Evaluate: $\sum_{n=1}^{10}n\cdot (\sum_{r=1}^{10}\frac{r^2}{r+n})$

Published on 16 Apr 2026 - 7:14

score 143 · Answer 2 · 2026-05-10 18:43:54

143

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Show that $(a^3+a+1)(b^3+b+1)(c^3+c+1)\le 27$

Published on 10 May 2026 - 18:43

score 51 · Answer 3 · 2026-04-12 13:50:26

51

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Sum coefficients

Published on 12 Apr 2026 - 13:50

score 841 · Answer 4 · 2026-05-10 18:45:47

841

Views

If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

Published on 10 May 2026 - 18:45

score 49 · Answer 5 · 2026-04-09 09:56:42

49

Views

an issue with an equation devised for the incremental update formula (summation)

Published on 09 Apr 2026 - 9:56

score 489 · Answer 6 · 2026-04-15 22:54:08

489

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Reducing an indicator function summation into a simpler form.

Published on 15 Apr 2026 - 22:54

score 179 · Answer 7 · 2026-04-11 17:37:53

179

Views

What is $\sum_{i=1}^{n}\frac{F_i}{i}$?

Published on 11 Apr 2026 - 17:37

score 3.8k · Answer 8 · 2026-04-17 14:16:47

3.8k

Views

Is difference of two consecutive sums of consecutive integers (of the same length) always square?

Published on 17 Apr 2026 - 14:16

score 1k · Answer 9 · 2026-04-17 01:27:55

1k

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Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Published on 17 Apr 2026 - 1:27

score 147 · Answer 10 · 2026-04-15 16:21:52

147

Views

Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$

Published on 15 Apr 2026 - 16:21

score 594 · Answer 11 · 2026-04-12 23:19:49

594

Views

Distribution of distances between points with complete spatial randomness

Published on 12 Apr 2026 - 23:19

score 56 · Answer 12 · 2026-04-11 07:19:59

56

Views

Interchanging sum and integral

Published on 11 Apr 2026 - 7:19

score 719 · Answer 13 · 2026-04-17 04:42:51

719

Views

Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$

Published on 17 Apr 2026 - 4:42

score 111 · Answer 14 · 2026-04-12 19:06:06

111

Views

Does $\sum_{k=0}^\infty\frac{\Gamma(r+2)}{k!\Gamma(r+2-k)}B_kn^{-k}$ converge, and if so to what?

Published on 12 Apr 2026 - 19:06

score 147 · Answer 15 · 2026-04-10 21:56:50

147

Views

Sum to closed form

Published on 10 Apr 2026 - 21:56

List Question

Evaluate: $\sum_{n=1}^{10}n\cdot (\sum_{r=1}^{10}\frac{r^2}{r+n})$

Show that $(a^3+a+1)(b^3+b+1)(c^3+c+1)\le 27$

Sum coefficients

If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

an issue with an equation devised for the incremental update formula (summation)

Reducing an indicator function summation into a simpler form.

What is $\sum_{i=1}^{n}\frac{F_i}{i}$?

Is difference of two consecutive sums of consecutive integers (of the same length) always square?

Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$

Distribution of distances between points with complete spatial randomness

Interchanging sum and integral

Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$

Does $\sum_{k=0}^\infty\frac{\Gamma(r+2)}{k!\Gamma(r+2-k)}B_kn^{-k}$ converge, and if so to what?

Sum to closed form

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