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What does the $\prod$ symbol mean? - Mathematics Stack Exchange
21 The symbol $\Pi$ is the pi-product It is like the summation symbol $\sum$ but rather than addition its operation is multiplication For example, $$ \prod_ {i=1}^5i=1\cdot2\cdot3\cdot4\cdot5=120 $$ The other symbol is the coproduct
meaning - What does prod issues mean in computer science and software . . .
DevOps engineers are those who are good at debugging, troubleshooting, analyzing prod issues and providing solutions Who have good hands on technologies like unix shell scripting, perl, SQL etc
calculus - Prove $\prod\limits_ {i=1}^n (x_i^n+1)\geq 2^ {n}$ for . . .
One way, I guess to see this, is that this procedure fixes $\prod_ {i=1}^nx_i$, and when taking the logarithm is equivalent to the averaging process Thus, we get the result
Is $\mathop {\Large\times}$ (\varprod) the same as $\prod$?
At first I thought this was the same as taking a Cartesian product, but he used the usual $\prod$ symbol for that further down the page, so I am inclined to believe there is some difference Does anyone know what it is? This old SE question shows the symbol I am referring to, but sadly does not provide an explanation
Finding the limit $\lim_ {x \to 0} \frac {1-\prod_ {i=1}^n\cos^ {1 i . . .
By L'Hospital: The derivative of the denominator is (by pulling one cosine at a time from the product) $$\sum_ {i=1}^n\frac {i\sin (ix)} {\cos (ix)}\prod_ {i=1}^n\cos (ix) $$ This still tends to $0$ so we differentiate a second time and get $$\sum_ {i=1}^n\frac {i^2} {\cos^2 (ix)}\prod_ {i=1}^n\cos (ix)-\left (\sum_ {i=1}^n\frac {i\sin (ix)} {\cos (ix)}\right)^2\prod_ {i=1}^n\cos (ix),$$ which
Why isnt the expectation of a discrete random variable defined as . . .
Why isn't the expectation of a discrete random variable defined as $\prod_ {x\in\operatorname {Im X}} x^ {P (X=x)}$? Ask Question Asked today Modified today
How to find $L=\prod\limits_ {n\ge1}\frac { (\pi 2)\arctan (n . . .
We have $$\begin {align*} L = \lim_ {N\to\infty} \prod_ {n=1}^ {N} \frac {\frac {\pi} {2}\arctan (n)} {\arctan (2n-1)\arctan (2n)} \\ = \lim_ {N\to\infty} \prod_ {n
If $\sum a_n^k$ converges for all $k \geq 1$, does $\prod (1 + a_n . . .
By definition, an infinite product $\\prod (1 + a_n)$ converges iff the sum $\\sum \\log(1 + a_n)$ converges, enabling us to use various convergence tests for infinite sums, and the Taylor expansion $
real analysis - Finding Value of the Infinite Product $\prod \Bigl (1 . . .
@DanPetersen: The friend said "the terms in the product" - that is, the numbers being multiplied together - have values less than $1$, and therefore the value of the product can never be $1$ This is correct An infinite product of positive terms that converges to $1$ must have some terms (not partial products, but terms) that are at least $1$
elementary number theory - Mathematics Stack Exchange
There are at least $p_n- 1$ primes between $p_n$ and $\prod_ {k=1}^n p_k$ · This is an exercise in Władysław Narkiewicz's book The Development of Prime Number Theory