Question

How do I deal with $\cos(n\pi /4)$ in this series?

score 3.7k · Answer 1 · 2026-04-12 08:11:45

3.7k

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How do I deal with $\cos(n\pi /4)$ in this series?

Published on 12 Apr 2026 - 8:11

score 279 · Answer 2 · 2026-04-16 00:43:29

279

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Finding the sum $\frac{x}{x+1} + \frac{2x^2}{x^2+1} + \frac{4x^4}{x^4+1} + \cdots$

Published on 16 Apr 2026 - 0:43

score 308 · Answer 3 · 2026-04-15 17:02:02

308

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How does one prove $\int_0^\infty \frac{\log(x)}{1 + e^{ax}} \, dx = -\frac{\log(2)(2\log(a) + \log(2))}{2a}$ for $a > 0$?

Published on 15 Apr 2026 - 17:02

score 108 · Answer 4 · 2026-04-13 22:23:38

108

Views

Under these conditions can I say that $\sum (a_{n}^{2} + b_{n}^{2})$ converges?

Published on 13 Apr 2026 - 22:23

score 267 · Answer 5 · 2026-04-16 12:03:42

267

Views

Uniform convergence of the series $\sum_{n=1}^{\infty} \frac{z^n}{n}.$

Published on 16 Apr 2026 - 12:03

score 63 · Answer 6 · 2026-04-12 17:33:54

63

Views

The convergence radius of a complex series its the same of his real and imaginary series?

Published on 12 Apr 2026 - 17:33

score 43 · Answer 7 · 2026-04-16 12:40:41

43

Views

Show that as $n\rightarrow \infty,$ $\frac{n^4}{3^n}\rightarrow 0$ linearly with rate $\frac{1}{3}$

Published on 16 Apr 2026 - 12:40

score 975 · Answer 8 · 2026-04-12 17:58:13

975

Views

Formal Power Series as Linear Operators

Published on 12 Apr 2026 - 17:58

score 117 · Answer 9 · 2026-04-15 06:32:45

117

Views

Is it possible to express explicitly the general term of the sequence $ I_n = \int_0^1 t^n \arctan t \, \mathrm{d} t \, $?

Published on 15 Apr 2026 - 6:32

score 118 · Answer 10 · 2026-04-15 12:14:23

118

Views

Power series, differential equations

Published on 15 Apr 2026 - 12:14

score 370 · Answer 11 · 2026-04-15 14:39:31

370

Views

Analize the convergence of $\sum z^n/n$

Published on 15 Apr 2026 - 14:39

score 147 · Answer 12 · 2026-04-13 16:13:21

147

Views

Compute $\log 3$ numerically using power series

Published on 13 Apr 2026 - 16:13

score 22 · Answer 13 · 2026-04-16 14:03:28

22

Views

Proof $P_c(x) + xP_c(x) = 1- P_b(x)$

Published on 16 Apr 2026 - 14:03

score 54 · Answer 14 · 2026-04-14 17:45:55

54

Views

Value of $p(y) = \sum_{n=0}^{\infty} \dfrac{2^n \cos(ny)}{n!}$

Published on 14 Apr 2026 - 17:45

score 1k · Answer 15 · 2026-04-11 05:19:02

1k

Views

Is a function that integrates to zero against all polynomials constant?

Published on 11 Apr 2026 - 5:19

List Question

How do I deal with $\cos(n\pi /4)$ in this series?

Finding the sum $\frac{x}{x+1} + \frac{2x^2}{x^2+1} + \frac{4x^4}{x^4+1} + \cdots$

How does one prove $\int_0^\infty \frac{\log(x)}{1 + e^{ax}} \, dx = -\frac{\log(2)(2\log(a) + \log(2))}{2a}$ for $a > 0$?

Under these conditions can I say that $\sum (a_{n}^{2} + b_{n}^{2})$ converges?

Uniform convergence of the series $\sum_{n=1}^{\infty} \frac{z^n}{n}.$

The convergence radius of a complex series its the same of his real and imaginary series?

Show that as $n\rightarrow \infty,$ $\frac{n^4}{3^n}\rightarrow 0$ linearly with rate $\frac{1}{3}$

Formal Power Series as Linear Operators

Is it possible to express explicitly the general term of the sequence $ I_n = \int_0^1 t^n \arctan t \, \mathrm{d} t \, $?

Power series, differential equations

Analize the convergence of $\sum z^n/n$

Compute $\log 3$ numerically using power series

Proof $P_c(x) + xP_c(x) = 1- P_b(x)$

Value of $p(y) = \sum_{n=0}^{\infty} \dfrac{2^n \cos(ny)}{n!}$

Is a function that integrates to zero against all polynomials constant?

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