Question

How Euler arrived at power series for $a^x$ and $\ln x$

score 280 · Answer 1 · 2026-05-10 16:05:13

280

Views

How Euler arrived at power series for $a^x$ and $\ln x$

Published on 10 May 2026 - 16:05

score 85 · Answer 2 · 2026-04-12 06:45:17

85

Views

Easiest way to show sequence $e^{\frac{1}{n}}$ converges to 1

Published on 12 Apr 2026 - 6:45

score 273 · Answer 3 · 2026-04-16 14:11:23

273

Views

On the series $\sum \limits_{n=-\infty}^{\infty} \frac{\cos n}{n^2+1}$.

Published on 16 Apr 2026 - 14:11

score 82 · Answer 4 · 2026-05-15 04:18:01

82

Views

Exchange of limit and sum for a uniformly convergent sequence

Published on 15 May 2026 - 4:18

score 141 · Answer 5 · 2026-05-11 09:36:32

141

Views

What would be the closed form of $n\cdot n + (n-2)\cdot(n-2) + (n-4)\cdot(n-4) + \dots$?

Published on 11 May 2026 - 9:36

score 52 · Answer 6 · 2026-04-10 00:25:55

52

Views

Sum of series with algebraic function

Published on 10 Apr 2026 - 0:25

score 2.5k · Answer 7 · 2026-04-10 21:31:22

2.5k

Views

Does this mathematical technique have a formal name? And why does it work?

Published on 10 Apr 2026 - 21:31

score 64 · Answer 8 · 2026-04-16 16:29:49

64

Views

Solve $a_n = a_{n-1} + n$, $a_0 = 0$, using generative function

Published on 16 Apr 2026 - 16:29

score 170 · Answer 9 · 2026-05-10 12:33:45

170

Views

Show that $3=\sqrt{1+2\sqrt{1+3\sqrt{1+4...}}}$

Published on 10 May 2026 - 12:33

score 72 · Answer 10 · 2026-04-16 14:47:23

72

Views

What method is most preferred to find nature of the series $\sum_{n=1}^{\infty} \frac{a^n}{a^n+x^n}$?

Published on 16 Apr 2026 - 14:47

score 389 · Answer 11 · 2026-04-11 07:06:42

389

Views

Difference between constant and random variable always equal to constans

Published on 11 Apr 2026 - 7:06

score 251 · Answer 12 · 2026-04-15 02:10:42

251

Views

Name of this recursively defined sequence of prime numbers?

Published on 15 Apr 2026 - 2:10

score 477 · Answer 13 · 2026-04-17 12:59:19

477

Views

A nice expression for $\int_0^{\pi/2} \left[\frac{1}{x \sin(x)}-\frac{1}{x^2}\right] \mathrm{d} x$

Published on 17 Apr 2026 - 12:59

score 213 · Answer 14 · 2026-04-15 19:21:28

213

Views

Why $\sum_{k=1}^m \left(\cos{\frac{2\pi k}{2m+1}}\right)^{(2m+1)^2}$ converges to $\sum_{k=1}^\infty e^{-2\pi^2k^2}$?

Published on 15 Apr 2026 - 19:21

score 504 · Answer 15 · 2026-04-13 18:58:11

504

Views

Does recursively replacing $\frac1n$ by $\frac1n(\frac12+\dots+\frac1{n+1})$ really converge to $\frac1e$?

Published on 13 Apr 2026 - 18:58

List Question

How Euler arrived at power series for $a^x$ and $\ln x$

Easiest way to show sequence $e^{\frac{1}{n}}$ converges to 1

On the series $\sum \limits_{n=-\infty}^{\infty} \frac{\cos n}{n^2+1}$.

Exchange of limit and sum for a uniformly convergent sequence

What would be the closed form of $n\cdot n + (n-2)\cdot(n-2) + (n-4)\cdot(n-4) + \dots$?

Sum of series with algebraic function

Does this mathematical technique have a formal name? And why does it work?

Solve $a_n = a_{n-1} + n$, $a_0 = 0$, using generative function

Show that $3=\sqrt{1+2\sqrt{1+3\sqrt{1+4...}}}$

What method is most preferred to find nature of the series $\sum_{n=1}^{\infty} \frac{a^n}{a^n+x^n}$?

Difference between constant and random variable always equal to constans

Name of this recursively defined sequence of prime numbers?

A nice expression for $\int_0^{\pi/2} \left[\frac{1}{x \sin(x)}-\frac{1}{x^2}\right] \mathrm{d} x$

Why $\sum_{k=1}^m \left(\cos{\frac{2\pi k}{2m+1}}\right)^{(2m+1)^2}$ converges to $\sum_{k=1}^\infty e^{-2\pi^2k^2}$?

Does recursively replacing $\frac1n$ by $\frac1n(\frac12+\dots+\frac1{n+1})$ really converge to $\frac1e$?

Trending Questions

Popular # Hahtags

Popular Questions