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When Carl Friedrich Gauss (1777 - 1855) was at school his teacher wanted time off and gave the class the following question to keep them busy: Add all the natural number from 1 to 100 together. A few seconds later the young Carl Gauss showed his blackboard to the teacher. On his blackboard he had written the correct answer! How did he add up the numbers so quickly?

When Carl Friedrich Gauss (1777 - 1855) was at school his teacher wanted time off and gave the class the following question to keep them busy: Add all the natural number from 1 to 100 together. A few seconds later the young Carl Gauss showed his blackboard to the teacher. On his blackboard he had written the correct answer! How did he add up the numbers so quickly?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Use the example above to deduce Gauss's theorem for the first 99 counting numbers 

his teacher When Carl Friedrich Gauss (1777 - 1855) was at school - wanted time off and gave the class the following question to keep them busy: Add all the natural number from 1 to 100 together. A few seconds later the young Carl Gauss showed his blackboard to the teacher. On his blackboard he had written the correct answer! How did he add up the numbers so quickly? Study the following example and try finding out what the young Gauss had done. S denotes the sum of the terms. S, =1+2+3+4+5+6+7+8+9 S, =9+8+7+6+5+4+3+2+1 2S, = 10 +10+10+10+10+10 +10+10+10 2S, = 9x10 %3D 2S, = 90 S, = 45 %3D
Transcribed Image Text:his teacher When Carl Friedrich Gauss (1777 - 1855) was at school - wanted time off and gave the class the following question to keep them busy: Add all the natural number from 1 to 100 together. A few seconds later the young Carl Gauss showed his blackboard to the teacher. On his blackboard he had written the correct answer! How did he add up the numbers so quickly? Study the following example and try finding out what the young Gauss had done. S denotes the sum of the terms. S, =1+2+3+4+5+6+7+8+9 S, =9+8+7+6+5+4+3+2+1 2S, = 10 +10+10+10+10+10 +10+10+10 2S, = 9x10 %3D 2S, = 90 S, = 45 %3D
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