Question

观察下列各式,找规律①3^3-1^2=4×2; ②4^2-2^2=4×3; ③5^2-3^2=4×4; ④6^2-4^2

Answer 1

(1)第5个等式是( 7^2-5^2=4×6 );

(2)第100个等式是( 102^2-100^2=4×101 );

(3)第N个等式是( (N+2)^2-N^2=4×(N+1) );

(4)第N个等式的正确性说明如下：

(N+2)^2-N^2=N^2+4N+4-N^2=4N+4=4×(N+1)