Question

1、观察下列算式：2^2-1^2=3=2x1+1 3^2-2^2=5=2x2+1 4^2-3^2=7=2x3+1 5^2

Answer 1

2^2-1^2=3=2x1+1 3^2-2^2=5=2x2+1 4^2-3^2=7=2x3+1 5^2-4^2=9=2x4+1……n^2-(n-1)^2=2n-1=2(n-1)+1(1) 把所得n个式子两边分别相加,左边=n^2-1^2右边=2(1+2+3+ ……+(n-1))+n-1（2）n^2-1=2(1+2+3+ ……+(n-1))+n-1...