老师在黑板上写出四个等式:1²+(1×2)²+2²=(1×2+1)²,2²+(2×3)²+3²=(2×3+1)²,3²+(3×4)²+4²=(3×4+1)²,4²+(4×5)²+5&
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 14:43:22
老师在黑板上写出四个等式:1²+(1×2)²+2²=(1×2+1)²,2²+(2×3)²+3²=(2×3+1)²,3
老师在黑板上写出四个等式:1²+(1×2)²+2²=(1×2+1)²,2²+(2×3)²+3²=(2×3+1)²,3²+(3×4)²+4²=(3×4+1)²,4²+(4×5)²+5&
老师在黑板上写出四个等式:1²+(1×2)²+2²=(1×2+1)²,2²+(2×3)²+3²=(2×3+1)²,3²+(3×4)²+4²=(3×4+1)²,4²+(4×5)²+5²=(4×5+1)²...
(1)请你对此提规律写出第2012个等式;
(2)请你类似的写第n个等式;
(3)证明第n个等式的正确性.
老师在黑板上写出四个等式:1²+(1×2)²+2²=(1×2+1)²,2²+(2×3)²+3²=(2×3+1)²,3²+(3×4)²+4²=(3×4+1)²,4²+(4×5)²+5&
(1)2012²+(2012X2013)²+2013²=(2012X2013+1)²
(2)n²+[n(n+1)]²+(n+1)²=[n(n+1)+1]²
(3)n²+[n(n+1)]²+(n+1)²
=n²+[n(n+1)]²+(n+1)²
=n²+n²(n+1)²+(n+1)²
=n²+(n²+1)(n+1)²
=n²+(n²+1)(n²+2n+1)
=n²+(n²+1)(n²+1+2n)
=n²+(n²+1)²+2n(n²+1)
=(n²+1)²+2n(n²+1)+n²
=(n²+1+n)²
=(n²+n+1)²
=[n(n+1)+1]²