What is Test: Definition and 1000 Discussions

## \sum_{n=0}^\infty \frac {(2n)!}{(n!)^2} ## ##\lim_{n \rightarrow +\infty} {\frac {a_{n+1}} {a_n}}## that becomes ##\lim_{n \rightarrow +\infty} {\frac { \frac {(2(n+1))!}{((n+1)!)^2}} { \frac {(2n)!}{(n!)^2}}}## ##\lim_{n \rightarrow +\infty} \frac {(2(n+1))!(n!)^2}{((n+1)!)^2(2n)!}##...

Below, I have already solved - I assume - correctly for question 1. Question 2, I am nearing to what I believe is the solution. Question 3, I simply have no idea where I should begin considering that it is interconnected with question 2. With that said, below is the lengthy and somewhat tedious...

To begin with, I posted this thread ahead of time simply because I thought it may provide me some insight on how to solve for another problem that I have previously posted here: https://www.physicsforums.com/threads/special-relativity-test-particle-inside-suns-gravitational-field.983171/unread...

Edit: This was split out of the space stuff and launch info thread. The in-flight abort of Dragon 2 is planned for Saturday (18th) 13:00 UTC, this is one day and 12 hours after my post. It is a 4 hour launch window, as this is a test it is quite possible that the launch is pushed back within...

Below is an attempted solution based off of another user's work on StackExchange: Source: [https://physics.stackexchange.com/questions/525169/special-relativity-test-particle-inside-the-suns-gravitational-field/525212#525212] To begin with, I will be using the following equation mentioned in...

Hey! :o In a study at $15$ children at the age of $10$ years the number of hours of television watching per week and the pounds above or below the ideal body weight were determined (high positive values ​​= overweight). Determine the simple linear regression equation by considering the...

I found that ρn = √(2n+1)/(n+1). Then, I found ρ = lim when n→∞ |(1/n) (√(2n+1))/((1/n) (n+1))| = 0 Based on this result I concluded the series converges; however, the book answer says it diverges. What am I doing wrong?

Hello everyone! I am trying to modelate a tensile test of dumbbell-shaped specimen under ACP PrePost and Static Structural modules. The laminate I am configuring consists of 6 laminas of E FiberGlass orientated +/-45°. For simplicity I am working with 1/4 of the geometry and the boundary...

After evaluating the integral I found the following: (1/3)tan-1(e∞/3) = (1/3)tan-1(∞) = (1/3)(nπ/2), where n is an odd number. In this case I found multiple solutions to the problem. How do you prove it converges?

Some functions have straight foward integrals, but they get complicated if you take the inverse of it. 1/f(x) for instance. The primitive of 1/x is ln(x). In this case it's easy to check that the integral of 1/x or ln(x) from 1 to infinite diverges. ##\int_1^\infty (\ln(x))^n dx## If n = 0, I...

I got the following expression: -(1/4)ln((n+2)/(n-2)) When I substitute "∞" in the expression I found it undefined. However, the book says the series converges. What am I doing wrong?

I am currently taking upper division physics, math, and materials science courses at a difficult US university. I never feel lost during lecture, read and comprehend the text, go above and beyond on problem sets, and can nearly do any problem in the book. Yet, when it comes time for the exam, I...

The SpaceX Starship Mk1 prototype has been damaged beyond repair 20 November 2019 during a cryogenic pressure test. Entire top been torn off. https://www.space.com/spacex-starship-prototype-anomaly-pressure-test.html

316 Ratio Test $\tiny{11.6.(4) } $ $$L=\sum_{n=1}^{\infty}\dfrac{\ln(n+1)}{n+1} $$ using the Ratio Test $$L=\displaystyle\lim_{n \to \infty} \left|\dfrac{a_{n+1}}{a_n}\right| =\lim_{n \to \infty}\dfrac{\ln((n+1)+1)}{((n+1)+1)} =\lim_{n \to...

Tensile tested 2 samples of 1018 unheat treated carbon steel, assumed to be very similar steel (bought from same place, same order, ect) but very different tensile test results. The results of the tensile test can be seen below as well as a few calculated values. I do not know what this would be...

Determine Convergence or divergence and test used $\displaystyle\sum_{n=1}^{\infty} \dfrac{1+4^n}{1+3^n}$ W|A says diverges using ratio test so $\therefore L=\lim_{n \to \infty}\left|\dfrac{a_n+1}{a_n}\right|>1$ Steps $\displaystyle L=\lim_{n \to \infty}\left|...

I am working on a personal project that I believe can increase the shelf life of milk in a refrigerator. I want to know if anyone knows any scientific ways of testing if milk is bad (due to bacterial growth) as I would prefer to avoid having my family sample a statistically significant sample...

Use the Ratio Test to determine whether the series is convergent or divergent $$\sum_{n=1}^{\infty}\dfrac{(-2)^n}{n^2}$$ If $\displaystyle\lim_{n \to \infty} \left|\dfrac{a_{n+1}}{a_n}\right|=L>1 \textit{ or } \left|\dfrac{a_{n+1}}{a_n}\right|=\infty...

Use the comparison test to determine if the series series convergences or divergences $$S_{6}=\sum_{n=1}^{\infty} \dfrac{1}{n^2 \ln{n} -10}$$ ok if i follow the example given the next step alegedly would be... $$\dfrac{1}{n^2 \ln{n} -10}<\dfrac{1}{n^2 \ln{n}}$$ $\tiny{242 UHM}$

Summary: Turing I have great respect for nearly all of Turing's work but as for the Turing Test I have a lot of problems. My life has taken me through many layers of the socio-economic spectrum, and I have learned a few things about my fellow humans that Turing may not have had the...

Hello all, I was working on some homework regarding testing for convergence and divergence of series and I was having trouble with a particular series (doesn't really matter which one) and tried almost all the methods; then tried the Integral Test, my series met the conditions of the...

Hi all, I have some doubts regarding the Kolmogorov test: I made a simple c++ program generating two samples of random numbers following a Landau distribution (I used the "hit and miss" method). I made the Kolmogorov test, in order to check the randomness of the generator, but I'm having some...

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After reading this NY Times article on the possibility of cloning pets becoming a viable business in China, I was wondering if it might also become an area where germline modification might be more extensively tested and worked out. Why this might happen in China: large size of domestic pet...

Usually for a charge Q we state that for each point in space there exists a potential, and we can calculate this, draw graphs of potential etc. However, if electric potential energy is a property of a system of two charges, and potential is PE for a 1C test charge, then how can we even define a...

Hi everyone. I'm studying Mechanics of Materials and I got some question about 'nominal/true strain'. First of all, I agree that in tensile test, nominal stress is always smaller than true stress σt > σn cause when the material specimen is being stretched, then the actual area of the...

I figure I could connect a high voltage source with a high impedance, and verify that it clamps that voltage. The easy way would require very careful consideration to keep it safe - that would be to use a 220V outlet connected through a 220K Ohm Resistor on each leg. Apply the current limited...

Does the real vacuum pressure/underpressure depends only on the amount of impurities? In the case of theoretical Torricelli vacuum test, when no purities left in the vacuum: Is the vacuum 0Pa at 1m height (with 760mm of Hg) and also the same at 10m height (also with 760mm of Hg) of the test...

If I have impact test data showing energy absorbed by notched specimen, how do I utilize this data while designing. In my case, i am trying to design the valve which closes by striking on valve seat, how do i use the impact test results for this design?

Hello, I am currently writing my thesis, where I have to investigate if a surface treatment increases the adhesion (between tape and a plastic surface). For this purpose, I have among other tests, performed a tensile test between the tape and plastic surface. The tensile test can be separated...

Hi there. I have some questions from the Ames test. I am following Wikipedia and a book to understand this concept. My understanding : Ames test is a fast and convenient test that uses auxotrophic bacteria (those that cannot grow in histidine lacking medium) to find out if some chemical is...

I learned that the confidence interval and a two sided hypothesis test (test for difference) agree if both have the same significance level. Is that also true for one sided hypothesis tests? For instance, must a right-tailed Hypothesis test with alpha = 0.05 agree with the 95% confidence level...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with the proof of Theorem 2.3.9 (a) ... Theorem 2.3.9 reads as follows: Now, we can prove Theorem 2.3.9 (a) using the Cauchy...

I am in a process of making a mathematical model of an automobile driveline validation procedure called "Driveline impact". In this test, after the engine in cranked, first gear is selected. While clutch pedal is still pressed, engine rpm is raised unto its max. torque deliverable speed. In this...

Ok I didn't understand how he derived the $\left[\begin{array}{c}-4/3\\1/3\\1 \end{array}\right]$ where the red correction is

Hello again, I swear ... I seem to struggle trying to decipher which ANOVA to use ... drives me crazy. In this study, I have 75 participants that are all varsity athletes. They all completed a survey that scored attentional style within 6 variables (BET, OET, BIT, OIT, NAR, RED). I am...

While SpaceX tested the engines of a Crew Dragon capsule something went wrong. A lot of smoke was released, no one was harmed. Unfortunately that is the end of official statements already. It was planned to do an in-flight abort test of Crew Dragon in June or July and a crewed flight (first...

Interesting video on DNA and privacy in today's world: Specifically folks in some instances can be identified from their relatives DNA. The worry of course is false positives placing you at a crime scene or of a sketchy insurance company profiling you and refusing coverage based on what...

I will be taking a very important Physics test next week based on advanced physics topics. I realized that generally i am able to solve the questions successfully on my own. But the problem is when i take mock exams i seem to get “panicked” and miss details, or use wrong values. After the exam I...

Hi everyone I hope you are well. Maybe as you know according to Behners-Fisher problem (unequal variance case of samples) there are some kind of approximations. I have recently covered the Satterthweiths Approximations and comprehended the logic of it. But I got stuck with the Cochran-Cox...

Hi everyone, initially I have seen that in order to analyze residuals for finite sample, Ljung - Box is defined as $$n*(n+2)*\sum_{n=0}^h p_k^2/(n-k)$$ where n is the sample size, $$p_k$$ is the sample autocorrelation at lag k, and h is the number of lags being tested. Actually I know the proof...

Hi, I am curious about: $$x^m \delta^{(n)}(x) = (-1)^m \frac {n!} {(n-m)!} \delta^{(n-m)}(x) , m \leq n $$ I understand the case where m=n and m>n but not this. Just testing the left hand side with m=3 and n=4 and integrating by parts multiple times, I get -6. With the same values, the...

Hi, according to ARMA model it is said that in order to check out white noise terms, Ljung-Box is applied involving sum of squared autocorrelations of errors with relevant lags. In short, sum of them is chi-square distribution but n-p-q degree of freedom when we have ARMA(p,0,q) model. My...

Hi, could you tell me how to calculate approximate value of impact force during Charpy test (pendulum hitting sample) ? The only formulas that can be found in literature for this test are maximum velocity ##v=\sqrt{2gh}## and work done for fracture ##K=mgR(cos \beta - cos \alpha)##. But it...

I want test my street lamp get lumen, lumen efficiency and color temperature, how can I get these data？

Homework Statement Hello, I was given 2 sets of data, showing 20 temperature values and 35 temperature values respectively. The data sets look like below: Data 1 Data 2 Temperature Temperature 30.9...

Using paired t test, how should I pair these results? To calculate the delta values, should I use: downstream - upstream for both sep and apr ? or upstream (sep) - upstream (apr) and downstream (sep) - downstream (apr) ? Thanks

Homework Statement Test the following series for convergence or divergence. ##\sum_{n = 1}^{\infty} \frac {\sqrt n} {e^\sqrt n}## Homework Equations None that I'm aware of. The Attempt at a Solution I know I can use the Integral Test for this, but I was hoping for a simpler way.

I have 2 independent samples (groups), each group contains 10 experimental values of variable T and their standard deviations (errors). I need to do intergroup statistical analysis, i.e. to elucidate whether there is significant difference between 2 groups in terms of variable T. I chose...

Please see the attached images that reference the text. To my understanding, we wish to use the integral test to compare to a series to see if the series converges or diverges. In these two examples, we use ##\sum_{n=1}^\infty \frac{1}{n}## compared with ##\int_1^{k+1} \frac{1}{x}dx## and for...