Question

用含n的代数式表示这个规律3^2-1^2=8*15^2-3^2=8*27^2-5^2=8*39^2-7^2=8*4.计算

Answer 1

3^2-1^2=8*1

5^2-3^2=8*2

7^2-5^2=8*3

9^2-7^2=8*4

.

(2n+1)^2-(2n-1)^2

=(2n+1+2n-1)(2n+1-2n+1)

=4n*2

=8n

计算2001^2-1999^2

=8*1000

=8000