SUEC 高中 Adv Maths (GP Sum to Infinity).pptx
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Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook suitable for SUEC (Maths), SPM (Maths and Add Maths) too
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https://tinyurl.com/ycjp8r7u
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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.
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Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
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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SUEC 高中 Adv Maths (GP Sum to Infinity).pptx
- 1. 𝒑𝒈 𝟏𝟑𝟏
- 2. 𝒑𝒈 𝟏𝟑𝟐
- 3. 𝒑𝒈 𝟏𝟑𝟑
- 4. 𝒑𝒈 𝟏𝟑𝟒
- 5. 𝒑𝒈 𝟏𝟑𝟒 A dot over a number represents a recurring number.
- 7. 𝒑𝒈 𝟏𝟑𝟒
- 8. 𝒑𝒈 𝟏𝟑𝟒 2 = 2 1 2 2 2 = 2 × 2 1 2 1 2 = 2 1 2 × 2 1 4 2 2 2 = 2 2 × 2 1 2 1 2 1 2 = 2 1 2 × 2 1 4 × 2 1 8 = 2 1 2 + 1 4 + 1 8 2 2 2 . . . = 2 1 2 + 1 4 + 1 8 + ... = 2 1 2 1− 1 2 = 2
- 9. 𝒑𝒈 𝟏𝟑𝟒 The area of equilateral triangle ABC is S. Connect the midpoints of its sides to the midpoints of the triangles. Get a small triangle, then connect the small triangles, sum of infinite triangles = ? 𝑎𝑠𝑠𝑢𝑚𝑒 𝐴𝐴𝐵𝐶 = 𝑆 = 1 𝐴𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 ∆ = 𝑆 4 = 1 4 𝑟 = 1 4 𝑆∞ = 1 1 − 1 4 = 4 3
- 10. 𝒑𝒈 𝟏𝟑𝟓
- 11. 𝒑𝒈 𝟏𝟑𝟓 − 𝟏𝟑𝟔
- 12. 𝒑𝒈 𝟏𝟑𝟕
- 13. 𝒑𝒈 𝟏𝟑𝟕
- 14. 𝒑𝒈 𝟏𝟑𝟕
- 15. 𝒑𝒈 𝟏𝟑𝟕
- 16. 𝒑𝒈 𝟏𝟑𝟕 = 4𝑛3 + 4𝑛 − 6𝑛2 − 𝟏 = 4 1 4 𝑛2 𝑛 + 1 2 + 4 𝑛 𝑛 + 1 2 − 6 1 6 𝑛 𝑛 + 1 2𝑛 + 1 − 𝒏 = 𝑛2 𝑛 + 1 2 + 2𝑛 𝑛 + 1 − 𝑛 𝑛 + 1 2𝑛 + 1 − 𝑛 = 𝑛2 (𝑛2 + 2𝑛 + 1) + 2𝑛2 + 2𝑛 − 𝑛(2𝑛2 + 3𝑛 + 1 − 𝑛 = 𝑛4 + 2𝑛3 + 𝑛2 + 2𝑛2 + 2𝑛 − 2𝑛3 − 3𝑛2 − 𝑛 − 𝑛 = 𝑛4 = 4 𝑘=1 𝑛 𝑘3 + 4 𝑘=1 𝑛 𝑘 − 6 𝑘=1 𝑛 𝑘2 − 𝜮 𝟏
- 17. 𝒑𝒈 𝟏𝟑𝟖
Editor's Notes
- https://www.geogebra.org/m/pkt5kkbf