Question

Find the value of $(1-z)\left(1+\frac{z}{2}\right)\left(1-\frac{z}{3}\right)\left(1+\frac{z}{4}\right)\cdots$.

score 419 · Answer 1 · 2015-10-28 03:16:35

419

Views

Find the value of $(1-z)\left(1+\frac{z}{2}\right)\left(1-\frac{z}{3}\right)\left(1+\frac{z}{4}\right)\cdots$.

Published on 28 Oct 2015 - 3:16

score 493 · Answer 2 · 2026-03-30 03:51:33

493

Views

First non-zero digit

Published on 30 Mar 2026 - 3:51

score 515 · Answer 3 · 2026-03-19 23:13:01

515

Views

Evaluate $A_0=\dfrac{3}{4}$, and $A_{n+1}=\dfrac{1+\sqrt{A_n}}{2}$

Published on 19 Mar 2026 - 23:13

score 943 · Answer 4 · 2015-11-09 14:59:11

943

Views

Limit of a sum of infinite series

Published on 09 Nov 2015 - 14:59

score 119 · Answer 5 · 2026-03-30 14:57:40

119

Views

What does this product converges to?

Published on 30 Mar 2026 - 14:57

score 118 · Answer 6 · 2026-03-23 00:40:31

118

Views

Why is the infinite product of this quotient of $\sin$'s equal to $\left(\frac{3}{\pi}\right)^{2}$[SOLVED]

Published on 23 Mar 2026 - 0:40

score 354 · Answer 7 · 2026-03-26 00:56:29

354

Views

Is $\prod_{n=1}^\infty P_{2n-1}$ regularizable?

Published on 26 Mar 2026 - 0:56

score 82 · Answer 8 · 2015-11-18 19:36:02

82

Views

Prove that $\prod\limits_{k=0}^n\frac{3k+1}{3k+2}\to0$ by elementary means

Published on 18 Nov 2015 - 19:36

score 2.1k · Answer 9 · 2015-11-19 21:20:51

2.1k

Views

Joint distribution of an infinite collection of random variables?

Published on 19 Nov 2015 - 21:20

score 69 · Answer 10 · 2026-03-29 16:23:17

69

Views

A variation of Viète's formula -- an infinite product of nested radicals

Published on 29 Mar 2026 - 16:23

score 195 · Answer 11 · 2026-03-29 03:23:57

195

Views

How to prove this infinite product identity?

Published on 29 Mar 2026 - 3:23

score 726 · Answer 12 · 2015-11-22 19:29:08

726

Views

Closed form of the integral ${\large\int}_0^\infty e^{-x}\prod_{n=1}^\infty\left(1-e^{-24\!\;n\!\;x}\right)dx$

Published on 22 Nov 2015 - 19:29

score 328 · Answer 13 · 2015-11-25 22:26:13

328

Views

Show that a martingale is not $L^1$ convergent

Published on 25 Nov 2015 - 22:26

score 276 · Answer 14 · 2015-11-26 13:49:50

276

Views

Pre measure for an infinite product of measure spaces

Published on 26 Nov 2015 - 13:49

score 220 · Answer 15 · 2015-11-29 23:30:17

220

Views

Infinite product $\prod\limits_{k=0}^\infty\sum\limits_{n=0}^9z^{10^kn} $ leading to $1/(1-z)$

Published on 29 Nov 2015 - 23:30

List Question

Find the value of $(1-z)\left(1+\frac{z}{2}\right)\left(1-\frac{z}{3}\right)\left(1+\frac{z}{4}\right)\cdots$.

First non-zero digit

Evaluate $A_0=\dfrac{3}{4}$, and $A_{n+1}=\dfrac{1+\sqrt{A_n}}{2}$

Limit of a sum of infinite series

What does this product converges to?

Why is the infinite product of this quotient of $\sin$'s equal to $\left(\frac{3}{\pi}\right)^{2}$[SOLVED]

Is $\prod_{n=1}^\infty P_{2n-1}$ regularizable?

Prove that $\prod\limits_{k=0}^n\frac{3k+1}{3k+2}\to0$ by elementary means

Joint distribution of an infinite collection of random variables?

A variation of Viète's formula -- an infinite product of nested radicals

How to prove this infinite product identity?

Closed form of the integral ${\large\int}_0^\infty e^{-x}\prod_{n=1}^\infty\left(1-e^{-24\!\;n\!\;x}\right)dx$

Show that a martingale is not $L^1$ convergent

Pre measure for an infinite product of measure spaces

Infinite product $\prod\limits_{k=0}^\infty\sum\limits_{n=0}^9z^{10^kn} $ leading to $1/(1-z)$

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