Question

How prove this inequality $\sum_{i=1}^{n}\sum_{j=1}^{n}\text{lcm}(i,j)\le\frac{n^3}{5}(n+4)$?

score 200 · Answer 1 · 2026-04-15 18:35:03

200

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How prove this inequality $\sum_{i=1}^{n}\sum_{j=1}^{n}\text{lcm}(i,j)\le\frac{n^3}{5}(n+4)$?

Published on 15 Apr 2026 - 18:35

score 357 · Answer 2 · 2026-04-22 16:21:47

357

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Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$

Published on 22 Apr 2026 - 16:21

score 111 · Answer 3 · 2026-04-14 06:27:21

111

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Product of two summations with two indices.

Published on 14 Apr 2026 - 6:27

score 169 · Answer 4 · 2026-04-09 20:45:48

169

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Finding the closed-form formula to a recurrence with summation of terms

Published on 09 Apr 2026 - 20:45

score 45 · Answer 5 · 2026-04-17 09:50:39

45

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Evaluate: $\sum_{j=1}^{k}\cos(j^{1/k})$

Published on 17 Apr 2026 - 9:50

score 329 · Answer 6 · 2026-04-16 08:49:43

329

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Proving $\sum_{k=0}^n\sum_{l=0}^k{n \choose k}^2{k \choose l}{n \choose l}{2n-l \choose n}=\sum_{k=0}^n {n \choose k}^2{n+k \choose k}^2$

Published on 16 Apr 2026 - 8:49

score 54 · Answer 7 · 2026-04-15 18:24:18

54

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Why is it true that "$\sum_{k,l\geq1}a_{kl}=\sum_{m\geq1}\sum_{k+l=m}a_{kl}$"?

Published on 15 Apr 2026 - 18:24

score 70 · Answer 8 · 2026-03-25 09:29:56

70

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sum of power floor $ S(n,m) = \sum_{i = 1}^{n} \Bigl \lfloor \frac{n}{i^m} \Bigr \rfloor i^m $

Published on 25 Mar 2026 - 9:29

score 151 · Answer 9 · 2026-04-26 05:30:46

151

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Multi Index Power Series

Published on 26 Apr 2026 - 5:30

score 133 · Answer 10 · 2026-04-13 21:41:45

133

Views

Closed form for summation involving ceil function

Published on 13 Apr 2026 - 21:41

score 99 · Answer 11 · 2026-04-14 00:41:13

99

Views

Combinatoric Polynomial Summing Proof

Published on 14 Apr 2026 - 0:41

score 85 · Answer 12 · 2026-04-10 16:24:44

85

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Finding a formula for $\sum_{k=1}^n(k^2-(k-1)^2)$

Published on 10 Apr 2026 - 16:24

score 135 · Answer 13 · 2026-04-10 13:33:40

135

Views

How should we evaluate such questions on limit of summation?

Published on 10 Apr 2026 - 13:33

score 199 · Answer 14 · 2026-04-09 07:30:38

199

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Triangle inequality in sum of summations

Published on 09 Apr 2026 - 7:30

score 194 · Answer 15 · 2026-04-09 02:08:36

194

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Sum of squared Fresnel sine integral

Published on 09 Apr 2026 - 2:08

List Question

How prove this inequality $\sum_{i=1}^{n}\sum_{j=1}^{n}\text{lcm}(i,j)\le\frac{n^3}{5}(n+4)$?

Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$

Product of two summations with two indices.

Finding the closed-form formula to a recurrence with summation of terms

Evaluate: $\sum_{j=1}^{k}\cos(j^{1/k})$

Proving $\sum_{k=0}^n\sum_{l=0}^k{n \choose k}^2{k \choose l}{n \choose l}{2n-l \choose n}=\sum_{k=0}^n {n \choose k}^2{n+k \choose k}^2$

Why is it true that "$\sum_{k,l\geq1}a_{kl}=\sum_{m\geq1}\sum_{k+l=m}a_{kl}$"?

sum of power floor $ S(n,m) = \sum_{i = 1}^{n} \Bigl \lfloor \frac{n}{i^m} \Bigr \rfloor i^m $

Multi Index Power Series

Closed form for summation involving ceil function

Combinatoric Polynomial Summing Proof

Finding a formula for $\sum_{k=1}^n(k^2-(k-1)^2)$

How should we evaluate such questions on limit of summation?

Triangle inequality in sum of summations

Sum of squared Fresnel sine integral

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