Question

Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n} \sum_{i=0}^j \frac{i^2+j^2}{n^4+ijn^2}$

score 70 · Answer 1 · 2020-06-03 21:43:11

70

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Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n} \sum_{i=0}^j \frac{i^2+j^2}{n^4+ijn^2}$

Published on 03 Jun 2020 - 21:43

score 159 · Answer 2 · 2020-06-05 05:53:37

159

Views

Limit of Darboux sums in $\mathbb{R}^n$

Published on 05 Jun 2020 - 5:53

score 49 · Answer 3 · 2020-06-05 19:59:21

49

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Relation between riemann sums of 3 functions

Published on 05 Jun 2020 - 19:59

score 218 · Answer 4 · 2026-03-26 14:23:08

218

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Proof regard to the function $ f\left(x\right)=\begin{cases} x^{2}\sin\left(\frac{1}{x^{2}}\right) & x\neq0\\ 0 & x=0 \end{cases} $

Published on 26 Mar 2026 - 14:23

score 56 · Answer 5 · 2020-06-07 13:00:01

56

Views

Integration with indicator function $I(x=0)$

Published on 07 Jun 2020 - 13:00

score 506 · Answer 6 · 2020-06-08 21:16:34

506

Views

Rewriting Riemann sum as integral

Published on 08 Jun 2020 - 21:16

score 91 · Answer 7 · 2020-06-09 07:47:50

91

Views

Limit $\lim_{n\to \infty} \frac{1}{n^{n+1}}\sum_{k=1}^n k^p$

Published on 09 Jun 2020 - 7:47

score 57 · Answer 8 · 2020-06-11 09:06:01

57

Views

Generalizing a Riemann sum by midpoints

Published on 11 Jun 2020 - 9:06

score 178 · Answer 9 · 2020-06-13 05:36:08

178

Views

Suface area calculus definition confusion?

Published on 13 Jun 2020 - 5:36

score 823 · Answer 10 · 2020-06-13 21:25:40

823

Views

Is the indicator function of rational numbers integrable?

Published on 13 Jun 2020 - 21:25

score 69 · Answer 11 · 2026-02-23 10:06:19

69

Views

calculating $\lim_{n\to\infty}\frac{1}{n}\sum_{i=-\frac{nf}{2}}^{\frac{nf}{2}}e^{-(\frac{1}{n^2}+\alpha)i^2}$

Published on 23 Feb 2026 - 10:06

score 105 · Answer 12 · 2020-06-27 13:42:24

105

Views

Calculating $\lim _{n\to \infty }\left(\frac{1\cdot n + 2\cdot(n-1) + 3\cdot (n-2)+ ... +1\cdot n}{n^2}\right)$?

Published on 27 Jun 2020 - 13:42

score 68 · Answer 13 · 2020-07-05 22:40:18

68

Views

If $L=\lim_{n \to \infty} \sum_{i=1}^{n-1} {\left(\frac{i}{n}\right)}^{2n}$ what is $\lfloor \frac{1}{L} \rfloor$

Published on 05 Jul 2020 - 22:40

score 150 · Answer 14 · 2020-07-11 05:46:44

150

Views

Finding $\lim_{n\to \infty}\left((1+\frac{1}{n^2})(1+\frac{2^2}{n^2})^2\cdots(1+\frac{n^2}{n^2})^n\right)^{\frac{1}{n}}$

Published on 11 Jul 2020 - 5:46

score 114 · Answer 15 · 2026-03-27 05:59:35

114

Views

On the sum of diameters of a partition covering a bounded set.

Published on 27 Mar 2026 - 5:59

List Question

Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n} \sum_{i=0}^j \frac{i^2+j^2}{n^4+ijn^2}$

Limit of Darboux sums in $\mathbb{R}^n$

Relation between riemann sums of 3 functions

Proof regard to the function $ f\left(x\right)=\begin{cases} x^{2}\sin\left(\frac{1}{x^{2}}\right) & x\neq0\\ 0 & x=0 \end{cases} $

Integration with indicator function $I(x=0)$

Rewriting Riemann sum as integral

Limit $\lim_{n\to \infty} \frac{1}{n^{n+1}}\sum_{k=1}^n k^p$

Generalizing a Riemann sum by midpoints

Suface area calculus definition confusion?

Is the indicator function of rational numbers integrable?

calculating $\lim_{n\to\infty}\frac{1}{n}\sum_{i=-\frac{nf}{2}}^{\frac{nf}{2}}e^{-(\frac{1}{n^2}+\alpha)i^2}$

Calculating $\lim _{n\to \infty }\left(\frac{1\cdot n + 2\cdot(n-1) + 3\cdot (n-2)+ ... +1\cdot n}{n^2}\right)$?

If $L=\lim_{n \to \infty} \sum_{i=1}^{n-1} {\left(\frac{i}{n}\right)}^{2n}$ what is $\lfloor \frac{1}{L} \rfloor$

Finding $\lim_{n\to \infty}\left((1+\frac{1}{n^2})(1+\frac{2^2}{n^2})^2\cdots(1+\frac{n^2}{n^2})^n\right)^{\frac{1}{n}}$

On the sum of diameters of a partition covering a bounded set.

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