Chapter 1, Problem 1NT

NOW TRY THIS

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: $1^2+2^2+\mathrm{...}+{100}^2$

To determine

To explain:

The sum of $1^2+2^2+\mathrm{...}+{100}^2$ by Gauss’s approach.

Answer to Problem 1NT

Solution:

Gauss’s approach does not work for the squares.

Explanation of Solution

Given:

$1^2+2^2+\mathrm{...}+{100}^2$ 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: $3^2+{98}^2\ne 4^2+{97}^2$.