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=4×5;
(1)第5个等式是( );
(2)第100个等式是( );
(3)第N个等式是( );
(4)说明第N个等式的正确性。

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)

Answer 2

(1)第5个等式7^2-5^2=4×6
(2)第100个等式 102^2-100^2=4×101
(3)第N个等式 (N+2)^2-N^2=4×(N+1)
(4)第N个等式的正确性说明
(N+2)^2-N^2=N^2+4N+4-N^2=4N+4=4×(N+1)

Answer 3

7^2-5^2=4X6
102^2-100^2=100x101
(n+2)^2-n^2=n(n+1)