Question

Evaluate $\lim \limits_{n \to \infty} \sum_{k=1}^{\lfloor n/2 \rfloor} \frac {n^2}{n^2-k^2}$

score 86 · Answer 1 · 2026-04-16 07:14:04

86

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Evaluate $\lim \limits_{n \to \infty} \sum_{k=1}^{\lfloor n/2 \rfloor} \frac {n^2}{n^2-k^2}$

Published on 16 Apr 2026 - 7:14

score 418 · Answer 2 · 2026-04-15 13:16:32

418

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Necessary condition of convergence of series and power series

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score 388 · Answer 3 · 2026-04-14 06:03:36

388

Views

How to prove that $\sum_{n=1}^\infty\frac{\sin n\cdot\sin n^2}{n}$ converges?

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score 150 · Answer 4 · 2026-04-13 10:14:04

150

Views

Divergent sequence which is always greater than its limsup?

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score 67 · Answer 5 · 2026-04-15 18:00:01

67

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score 495 · Answer 6 · 2026-04-12 23:40:02

495

Views

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score 67 · Answer 7 · 2026-04-14 16:16:04

67

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study of the convergence of the numerical series

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score 240 · Answer 8 · 2026-04-15 10:49:13

240

Views

$\alpha$ for uniform convergence $\sum \frac{x^\alpha}{1+n^2x^2}$

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score 358 · Answer 9 · 2026-04-14 11:19:53

358

Views

Conditionally convergence $\sum_\limits{n=1}^{\infty}(-1)^n\frac{\ln n}{n}$?

Published on 14 Apr 2026 - 11:19

score 62 · Answer 10 · 2026-04-15 00:43:06

62

Views

Closed sequence for an alternating pattern

Published on 15 Apr 2026 - 0:43

score 434 · Answer 11 · 2026-04-12 11:41:14

434

Views

Variation of a Beatty Sequence

Published on 12 Apr 2026 - 11:41

score 357 · Answer 12 · 2026-04-14 21:48:18

357

Views

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score 126 · Answer 13 · 2026-04-29 12:52:23

126

Views

Evaluation of infinite series of ratios (with denominators given as finite products) in terms of rational numbers and $\pi\sqrt3$

Published on 29 Apr 2026 - 12:52

score 3.6k · Answer 14 · 2026-04-13 00:18:35

3.6k

Views

If the sum of the tail of a series goes to $0$, must the series converge?

Published on 13 Apr 2026 - 0:18

score 60 · Answer 15 · 2026-04-12 02:05:20

60

Views

Floor value of sum whose general term satisfy recursive relation.

Published on 12 Apr 2026 - 2:05

List Question

Evaluate $\lim \limits_{n \to \infty} \sum_{k=1}^{\lfloor n/2 \rfloor} \frac {n^2}{n^2-k^2}$

Necessary condition of convergence of series and power series

How to prove that $\sum_{n=1}^\infty\frac{\sin n\cdot\sin n^2}{n}$ converges?

Divergent sequence which is always greater than its limsup?

Find all function $f:\Bbb{N}_0 \rightarrow \Bbb{N}_0 $ satisfying the equation $f(f(n) + f(n) = 2n +3k,$ where $k$ is a fixed natural number

Interesting sequence involving prime numbers jumping on the number line.

study of the convergence of the numerical series

$\alpha$ for uniform convergence $\sum \frac{x^\alpha}{1+n^2x^2}$

Conditionally convergence $\sum_\limits{n=1}^{\infty}(-1)^n\frac{\ln n}{n}$?

Closed sequence for an alternating pattern

Variation of a Beatty Sequence

Finite summation of series involving factorials and exponentials

Evaluation of infinite series of ratios (with denominators given as finite products) in terms of rational numbers and $\pi\sqrt3$

If the sum of the tail of a series goes to $0$, must the series converge?

Floor value of sum whose general term satisfy recursive relation.

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