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Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
inequality
induction
products
Limit of $\prod\limits_{k=2}^n\frac{k^3-1}{k^3+1}$
calculus
sequences-and-series
limits
products
infinite-product
Proving $(1+\frac 1n)^{n} = 1 + \sum_{k=1}^n({\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn))}$ using the binomial theorem
summation
products
binomial-theorem
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
inequality
convergence-divergence
induction
products
Mathematical induction problem: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$
inequality
induction
factorial
products
Proving: $\cos A \cdot \cos 2A \cdot \cos 2^{2}A \cdot \cos 2^{3}A ... \cos 2^{n-1}A = \frac { \sin 2^n A}{ 2^n \sin A } $
trigonometry
products
A "fast" way for computing $ \prod \limits_{i=1}^{45}(1+\tan i^\circ) $?
trigonometry
products
Infinite products - reference needed!
complex-analysis
reference-request
products
infinite-product
Why is the cartesian product so categorically robust?
soft-question
category-theory
products
How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
limits
products
What is to geometric mean as integration is to arithmetic mean?
integration
arithmetic
average
products
How to prove those "curious identities"?
trigonometry
products
Is there a simple way to expand the following Product Sum?
combinatorics
polynomials
summation
products
Evaluating the infinite product $\prod\limits_{k=2}^\infty \left ( 1-\frac1{k^2}\right)$
sequences-and-series
limits
closed-form
products
infinite-product
Product of cosines: $ \prod_{r=1}^{7} \cos \left(\frac{r\pi}{15}\right) $
algebra-precalculus
geometry
trigonometry
products
When is an infinite product of natural numbers regularizable?
sequences-and-series
reference-request
divergent-series
products
regularization
Does multiplying all a number's roots together give a product of infinity?
recreational-mathematics
real-numbers
radicals
products
infinite-product
Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$
real-analysis
sequences-and-series
analysis
products
infinite-product
Is $0! = 1$ because there is only one way to do nothing?
factorial
products
Is there an "inverted" dot product?
linear-algebra
abstract-algebra
vectors
terminology
products
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