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, …

Dec 28, 2013 · 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_ …

Thus, if we apply Kirchhoff's theorem, we get $$\prod_ {m=1}^ {n-1} 4\sin^2 (\frac {m\pi} {n}) = n^2.$$ By taking square root and dividing both sides by $2^ {n-1}$, we get the desired formula.

Sep 13, 2016 · Compute: $$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?

Sep 10, 2024 · 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 …

Aug 20, 2025 · Please edit to include your efforts. If, as you suggest, you know a proof of the statement involving $1$, why not include it? Presumably it sheds some light on how to …

Nov 1, 2024 · There are simple reasons for the others - it is that $1$ and $4$ are squares of integers.

Jan 17, 2025 · $$ \prod_ {p \leq x} p \geq\prod_ {\sqrt {x} < p \leq x} p \geq \left (\sqrt {x}\right)^ {\pi (x) - \pi (\sqrt {x})} \ge e^ {\frac1 {2} (\frac {1} {2} x - 4 \sqrt {x})}, $$ But I have no idea what to …

Sep 2, 2024 · 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.

Mar 29, 2023 · $$\begin {aligned}Q &= \prod_ { (i,j) \in A} (1-a_ia_j) \\ &= \sum_ {k=0}^ {|A|} \sum_ {S \subset A}^ {|S| = k} (-1)^k\ C_S \prod_ { (i,j) \in S} a_ia_j\\ \end {aligned}$$