The Balmer series is characterized by the electron transitioning from n ¡Ý 3 to n = 2‚ where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-¦Á‚ 4 to 2 is H-¦Â‚ 5 to 2 is H-¦Ã‚ and 6 to 2 is H-¦Ä. As the spectral lines associated with this series are located in the visible part of the electromagnetic spectrum‚ these lines are historically referred to as H-alpha‚ H-beta‚ H-gamma and
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Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln 2) lim = ‚ R!1 1 p 1 p 1 p so does the series. 2. (18 pts.) Find the in…nite sum 1 : n (n + 2) n=1 Solution: See that 1 1 = n (n + 2) n 1 n+2 1 X 8 R < ln ujln 2 ln 1 ln R du = 1 p : u p up 1 ln 2 hence 1 n (n + 2) n=1 k X
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TIME SERIES ANALYSIS Introduction Economic and business time series analysis is a major field of research and application. This analysis method has been used for economic forecasting‚ sales forecasting‚ stock market analysis and company internal control. In this paper‚ we will talk about time series and review techniques that are useful for analyzing time series data. Definition of Time Series and Time Series Analysis Time series is an ordered sequence of values of a variable at equally spaced
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Title of Experiment: An Activity Series Lab MSDS: Copper‚ Cu(s) Stability- Stable. Incompatible with strong acids‚ active halogen compounds‚ chlorine‚ fluorine‚ iodine‚ bromine‚ ammonia. May react explosively with strong oxidizing agents. Toxicology-Dust may cause respiratory irritation. Personal Protection- Suitable ventilation if handling powder. Zinc‚ Zn(s) Stability-Stable. Incompatible with amines‚ cadmium‚ sulfur‚ chlorinated solvents‚ strong acids‚ strong bases. Air and moisture
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Kiwi Series #1 My choice of artwork for this essay is titled Kiwi Series # 1. This painting is made by Dennis Wojtkiewicz in 2005. The size of this painting is 36 by 66 inches. The medium used in this painting is the oil on canvas. I chose this painting because it appeals to my sense of aesthetics and also it has the most interesting use of texture. This painting is an excellent example of our sight being able to activate other senses. The presentation of the translucent fruit and fuzzy skin is
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BMW: THE 7-SERIES PROJECT mary lou Brief History of Bayerische Motoren Werke: BMW‚ a German company is a producer of automobiles and motorcycles. Designed as an aircraft manufacturer and originally founded in 1913 by Karl Fredrich Rapp‚ the company was commissioned to build the V-12 engine for Austria-Hungary. In need of extra financing‚ Rapp reconstructed the company as the Bayerische Motoren Werke. In 1917‚ Rapp left the company and it was taken over by Austrian Franz Josef Popp who
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through networks. The resultant output signal is dependent on the properties of both the input signal and the processes acting on the signal. This is a laboratory Report will be focusing on using Fourier series to analyze waveforms and the synthesis of waveforms. The report highlights Fourier series analysis is a simple effective approach to analyse periodic signals. It will guide the reader through an experiment conducted in a lab to examine the effects of using Fourier analysis on signals and their
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Fibonacci sequence in arithmetic sequence The Fibonacci sequence is a series of numbers in which each number is the sum of the previous two. It starts with 0 and 1‚ which equals 1. Then 1 plus 2 equals 3‚ 2 plus 3 equals 5‚ and so on. n mathematical terms‚ the sequence Fn of Fibonacci numbers is defined by the recurrence relation With seed values[1] The Fibonacci numbers are represented practically everywhere. In the petals on a flower‚ or the arrangement of leaves along a stem‚ you
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December 2008 SDL SERIES‚ ARTICLE #4 SDL Series - Article #4: Threat Modeling at Microsoft In this fourth article in the series‚ we examine how Microsoft uses a technique known as “threat modeling” to detect design issues that could result in product vulnerabilities. Threat modeling is one component of the Microsoft Security Development Lifecycle (SDL). Content The Microsoft SDL What is Threat Modeling? A Security Frame of Mind The Threat Modeling Process Mitigating Threats Threat Modeling
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[pic] Fourier Series: Basic Results [pic] Recall that the mathematical expression [pic] is called a Fourier series. Since this expression deals with convergence‚ we start by defining a similar expression when the sum is finite. Definition. A Fourier polynomial is an expression of the form [pic] which may rewritten as [pic] The constants a0‚ ai and bi‚ [pic]‚ are called the coefficients of Fn(x). The Fourier polynomials are [pic]-periodic functions. Using the trigonometric
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