Question

观察下列一组算式3^2-1^2=8=8*1,5^2-3^2=16=8*2,7^2-5^2=24=8*3

Answer 1

：（2n+1）²-（2n-1）²=8n（n为正整数）．

验证：（2n+1）²-（2n-1）²=（4n²+4n+1）-（4n²-4n+1）=8n．