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Product formula

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#calculus #number-theory #products
337
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Prove that$(1-\omega+\omega^2)(1-\omega^2+\omega^4)(1-\omega^4+\omega^8)…$ to 2n factors$=2^{2n}$

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#sequences-and-series #algebra-precalculus #complex-numbers #roots #products
162
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Is my formula for the coefficients of $\prod_{i=1}^n (x-a_i)$ correct?

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#abstract-algebra #products #cyclotomic-polynomials
138
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Morrie's law with sines

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#trigonometry #products
68
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Hovey book Model Categories

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#category-theory #products #model-categories
217
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Upper bound for $\prod\limits_{k = 1}^{n}\left( 1 - x^{k+1}\right)$

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#sequences-and-series #products #upper-lower-bounds
107
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Product Notation Problem

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#notation #products
60
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Any way to compute this serie?

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#sequences-and-series #binomial-coefficients #products
35
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Solving For Value in Product Series

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#sequences-and-series #derivatives #products
58
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Let $a_1 = 1$ and $a_n = n(a_{n-1}+1)$ for $n=2,3,..$; find $\lim_{n\to\infty}(1+1/a_1)(1+1/a_2)\cdot\ldots\cdot(1+1/a_n)$

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#limits #products
274
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The sequence $A_n=\prod_{k=1}^n\left(1+\frac{k}{n^2}\right)$ is decreasing

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#real-analysis #sequences-and-series #inequality #products
1.7k
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Inverse of product of 2 or more functions

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#algebra-precalculus #products #inverse-function
68
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Reasoning about the upper limit of an inequality that involves exponents

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#inequality #integers #products
68
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Is there an easy way of seeing that this sum is $0$?

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#algebra-precalculus #summation #arithmetic #products
119
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Limit related to $ f(x) = \prod_{i = 1}^x \left( \sin\left( i \frac{\pi}{n}\right) + \frac{5}{4}\right) $?

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#real-analysis #limits #trigonometry #asymptotics #products

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