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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ACTIVITY SERIES The activity series of metals is an list of metals ranked in order of decreasing reactivity to displace hydrogen gas from water and acid solutions. It can also be used to predict which metals will displace other metals in aqueous solutions. In introductory chemistry‚ the reactivity series or activity series is an empirical series of metals‚ in order of "reactivity" from highest to lowest. It is used to summarize information about the reactions of metals with acids and water‚ single
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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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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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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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(Values and attitudes) 5. Develop problem solving skills (Generic skills) Teaching power point‚ Activity worksheet‚ Visualizer‚ Computer‚ Pen‚ Pencil‚ Drawing paper Teaching materials: Time Learning Objectives mins 2 ! Introduction 10 ! First settle student learning and emotional
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Drawing the Color Line Drawing the Color Line by Howard Zinn the second chapter from A People’s history of the United States. The authors writes this chapter to explain racism and how it started‚ “a continent were we can trace the coming of the first whites and the first blacks-might supply at least a few clues” he wants to use history to try to explain why it started. In this chapter Howard Zinn gives us an insight on Slavery and racism in the early 17th century of America. This chapter does
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DRAW 111-Technical Drawing with CAD INFORMATION SHEET 1 The Graphic Language 1. Drawing is a graphic representation of real thing an idea or proposed design. 2. Drafting began when the early people started drawing objects on earth sand and stone 3. Drafting accurate manual or computerized presentation of working plans and detailed drawings. 4. CAD stands for computer aided drawing 5. Lettering is a very important part of drawing 6. Alphabet of lines examples of these
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Special Education Services. On Jason’s current evaluations and assessment information‚ on the Woodcock Johnson IV Test of Cognitive Abilities‚ Jason’s scored a 90 on for General Intellectual Ability‚ which falls in the average range. For the Autism Diagnostic Observation Schedule-2nd Edition (ADOS-2)‚ Jason’s overall total score was 26‚ which shows a very elevated score‚ and indicates a classification of autism. Strengths: Jason can state his first and last name‚ identify body parts‚ name colors
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