Sample Solution from
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Chapter 1
Problem 1NT
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Textbook Problem

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Explain whether the approach in Gauss’s Problem of writing the sum backward and applying the strategy look for a pattern will or will not work in finding the sum: 1 2 + 2 2 + ... + 100 2

Expert Solution
To determine

To explain:

The sum of 12+22+...+1002 by Gauss’s approach.

Answer

Solution:

Gauss’s approach does not work for the squares.

Explanation of Solution

Given:

12+22+...+1002 apply Gauss’s approach.

Approach:

Gauss’s approach is a method listed the sum from front and wrote the same sum from backward and the equal result.

Gauss’s approach for the sum of squares does not work because the sums change

For example: 32+98242+972.

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