Question

How do i represent an infinite series as an integral? (complex numbers)

score 84 · Answer 1 · 2026-04-08 17:48:57

84

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How do i represent an infinite series as an integral? (complex numbers)

Published on 08 Apr 2026 - 17:48

score 96 · Answer 2 · 2026-05-16 00:50:05

96

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Evaluate $\lim_{n\to \infty} \sum_{r=1}^n {\frac{r^4}{4r^2-1}}$

Published on 16 May 2026 - 0:50

score 303 · Answer 3 · 2026-04-15 17:07:37

303

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Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Published on 15 Apr 2026 - 17:07

score 88 · Answer 4 · 2026-04-12 20:30:57

88

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Convergence of $\sum_{n=1}^\infty \frac{\ln^k(n) }{n^a}$

Published on 12 Apr 2026 - 20:30

score 76 · Answer 5 · 2026-04-14 21:45:54

76

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Sum of a finite arithmetic sequence

Published on 14 Apr 2026 - 21:45

score 177 · Answer 6 · 2026-05-16 00:51:03

177

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Find the limit of $\lim _{ n\rightarrow \infty }{ \sum _{ k=1 }^{ n }{ \frac { \sqrt { { n }^{ 2 } - { k }^{ 2 } } } { { n }^{ 2 } } } } $

Published on 16 May 2026 - 0:51

score 403 · Answer 7 · 2026-05-11 09:47:55

403

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How show that $\sum_{j=0}^\infty \frac{(-1)^j\binom{\frac12}{j}}{{2j+1}}=\frac{\pi}4$

Published on 11 May 2026 - 9:47

score 209 · Answer 8 · 2026-04-14 00:28:02

209

Views

Prove sequence (of integrals) is bounded.

Published on 14 Apr 2026 - 0:28

score 199 · Answer 9 · 2026-04-17 00:26:39

199

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convergence of sequence defined recursively $\frac{2}{a_{n+2}}=\frac{1}{a_{n+1}}+\frac{1}{a_n}$

Published on 17 Apr 2026 - 0:26

score 107 · Answer 10 · 2026-04-16 13:10:17

107

Views

Prove $\sum$ and $\int$ are interchangeable in this proof

Published on 16 Apr 2026 - 13:10

score 36 · Answer 11 · 2026-04-15 18:17:20

36

Views

Length of covering $2D$ Grid circles

Published on 15 Apr 2026 - 18:17

score 272 · Answer 12 · 2026-04-15 09:30:06

272

Views

Convergence of $ \sum _ { n = 1 } ^ { \infty } \frac { n ! n ^ { n } } { ( 2 n ) ! } $

Published on 15 Apr 2026 - 9:30

score 156 · Answer 13 · 2026-05-15 22:35:46

156

Views

Interchanging a limit and an infinite alternate series

Published on 15 May 2026 - 22:35

score 162 · Answer 14 · 2026-05-11 01:05:03

162

Views

Expectation of a function of a Poisson random variable

Published on 11 May 2026 - 1:05

score 194 · Answer 15 · 2026-04-11 18:15:52

194

Views

Cesaro means of a positive sequence

Published on 11 Apr 2026 - 18:15

List Question

How do i represent an infinite series as an integral? (complex numbers)

Evaluate $\lim_{n\to \infty} \sum_{r=1}^n {\frac{r^4}{4r^2-1}}$

Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Convergence of $\sum_{n=1}^\infty \frac{\ln^k(n) }{n^a}$

Sum of a finite arithmetic sequence

Find the limit of $\lim _{ n\rightarrow \infty }{ \sum _{ k=1 }^{ n }{ \frac { \sqrt { { n }^{ 2 } - { k }^{ 2 } } } { { n }^{ 2 } } } } $

How show that $\sum_{j=0}^\infty \frac{(-1)^j\binom{\frac12}{j}}{{2j+1}}=\frac{\pi}4$

Prove sequence (of integrals) is bounded.

convergence of sequence defined recursively $\frac{2}{a_{n+2}}=\frac{1}{a_{n+1}}+\frac{1}{a_n}$

Prove $\sum$ and $\int$ are interchangeable in this proof

Length of covering $2D$ Grid circles

Convergence of $ \sum _ { n = 1 } ^ { \infty } \frac { n ! n ^ { n } } { ( 2 n ) ! } $

Interchanging a limit and an infinite alternate series

Expectation of a function of a Poisson random variable

Cesaro means of a positive sequence

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