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?

Name: 1. Use the example above to deduce Gauss's theorem for the first 99 co
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Description: 1. Use the example above to deduce Gauss's theorem for the first 99 counting numbers his teacherWhen Carl Friedrich Gauss (1777 - 1855) was at school -wanted time off and gave the class the following question to keep thembusy:Add all the natural numb

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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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

100%

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

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