Use induction to show that- for any integer n1 - i-1nii!-(n+1)!1.docx
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This document shows that the sum of the first n positive integers squared equals the factorial of n+1 minus 1. Specifically, it proves that for any positive integer n, the sum of i squared from i=1 to i=n equals (n+1)! minus 1 through mathematical induction.
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ุฉ ูู ุงูู ุณูุงูุฏ ุนูู ุฎุงุฑุทุฉ ุชุชุถู
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ูุน ุชูุฑูุนุงุช ู
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ุงุช ุงูุฌูุงุฒ ุงูููููู ุงูู
ุฐููุฑุฉ ูู ูุฐูู ุงูู
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ุฉ
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ุฉ ุญูุงูู ุนูููู
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ุฅู ุชุฏุนููู ุจุงูุฎูุฑ ูุงูุตุญุฉ ูุงูุนุงููุฉ ููุท
ูู ุงูุชูููู ุฒู
ูุงุฆู ูุฒู
ููุงุชู ุ ุฒู
ูููู
ู
ุญู
ุฏ ุงูุฐูุจู ๐๐
๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
Stack Memory Organization of 8086 Microprocessor
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๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
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ุชูุถูุญูุง ุจุดูู ุชูุตููู ุฌุฏุงู (ุชูุนุชุจุฑ ูุฏู ุงูุทุงูุจ ุฃู ุงูุทุงูุจุฉ ุจุฅููุง ู
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ุฉ ุชุดุฑุญ ููุณูุง ุจ ููุณูุง ุจุณ ุชููู ุชุนุงู ุงูุฑุงูู
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ุฉ ูู ุงูู ุณูุงูุฏ ุนูู ุฎุงุฑุทุฉ ุชุชุถู
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ุฅู ุชุฏุนููู ุจุงูุฎูุฑ ูุงูุตุญุฉ ูุงูุนุงููุฉ ููุท
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
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Chapter 6
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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