Question

If $y=\mathrm{e}^x\big(a\sin x+b\cos x\big)$, then express $y^{(n)}$ in terms of $y$ and $y'$.

score 79 · Answer 1 · 2026-03-24 22:07:35

79

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If $y=\mathrm{e}^x\big(a\sin x+b\cos x\big)$, then express $y^{(n)}$ in terms of $y$ and $y'$.

Published on 24 Mar 2026 - 22:07

score 195 · Answer 2 · 2026-04-11 20:51:55

195

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Convergence of a Cesaro sequence

Published on 11 Apr 2026 - 20:51

score 174 · Answer 3 · 2026-04-11 18:27:49

174

Views

How can I prove the values of convergence for $x^n/n$ without using the Ratio or Root test?

Published on 11 Apr 2026 - 18:27

score 460 · Answer 4 · 2026-03-25 01:18:49

460

Views

On the pseudo-Fibonacci and pseudo-Tribonacci sequences $A_n = \lceil e^{(n-1)/2}\rceil $ and $B_n = \lceil e^{\pi(n-1)/5}\rceil $

Published on 25 Mar 2026 - 1:18

score 277 · Answer 5 · 2018-02-15 16:13:41

277

Views

Geometric series $\sum_{n=0}^\infty x^n$ when $x=0$

Published on 15 Feb 2018 - 16:13

score 1k · Answer 6 · 2026-04-09 20:55:24

1k

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Countability of Fibonacci series

Published on 09 Apr 2026 - 20:55

score 56 · Answer 7 · 2026-04-07 02:11:38

56

Views

Digit counts in the multiples of $n$

Published on 07 Apr 2026 - 2:11

score 58 · Answer 8 · 2026-04-13 00:09:23

58

Views

Does the alternating series converge? [Leibniz criterion]

Published on 13 Apr 2026 - 0:09

score 31 · Answer 9 · 2026-03-26 12:53:36

31

Views

Finding the heaviest theoretical subpath of size ($n/2$), given a required cycle of size $n$ in a directed,weighted graph.

Published on 26 Mar 2026 - 12:53

score 175 · Answer 10 · 2026-04-12 22:04:34

175

Views

Does $\sum_{k=1}^\infty(-1)^k(\frac{k}{k+1})^k$ converge?

Published on 12 Apr 2026 - 22:04

score 126 · Answer 11 · 2026-04-12 22:49:47

126

Views

Prove that the sequence is bounded and subsequences converge

Published on 12 Apr 2026 - 22:49

score 264 · Answer 12 · 2026-04-12 12:43:18

264

Views

Is the space of all convergent sequences compact in the space of all bounded sequences($l^{\infty})$?

Published on 12 Apr 2026 - 12:43

score 90 · Answer 13 · 2026-04-12 07:43:12

90

Views

Is this sum rational or not? $1/(q+1)+1/(q+2)(q+1)...$ where $q$ is an integer

Published on 12 Apr 2026 - 7:43

score 119 · Answer 14 · 2026-04-09 00:08:17

119

Views

Where is positive or negative the function $\sum_{n=1}^\infty\frac{\mu(n)}{n}\left(\frac{\cos(nx)}{n}\right)^2$ over the set $[0,2\pi]$?

Published on 09 Apr 2026 - 0:08

score 1.4k · Answer 15 · 2026-04-06 17:20:16

1.4k

Views

Alternating series of primes

Published on 06 Apr 2026 - 17:20

List Question

If $y=\mathrm{e}^x\big(a\sin x+b\cos x\big)$, then express $y^{(n)}$ in terms of $y$ and $y'$.

Convergence of a Cesaro sequence

How can I prove the values of convergence for $x^n/n$ without using the Ratio or Root test?

On the pseudo-Fibonacci and pseudo-Tribonacci sequences $A_n = \lceil e^{(n-1)/2}\rceil $ and $B_n = \lceil e^{\pi(n-1)/5}\rceil $

Geometric series $\sum_{n=0}^\infty x^n$ when $x=0$

Countability of Fibonacci series

Digit counts in the multiples of $n$

Does the alternating series converge? [Leibniz criterion]

Finding the heaviest theoretical subpath of size ($n/2$), given a required cycle of size $n$ in a directed,weighted graph.

Does $\sum_{k=1}^\infty(-1)^k(\frac{k}{k+1})^k$ converge?

Prove that the sequence is bounded and subsequences converge

Is the space of all convergent sequences compact in the space of all bounded sequences($l^{\infty})$?

Is this sum rational or not? $1/(q+1)+1/(q+2)(q+1)...$ where $q$ is an integer

Where is positive or negative the function $\sum_{n=1}^\infty\frac{\mu(n)}{n}\left(\frac{\cos(nx)}{n}\right)^2$ over the set $[0,2\pi]$?

Alternating series of primes

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