找规律,并回答下列问题:已知:1²+2²+1²×2²=9=3²;2²+3²+2²×3²=49=7²;3²+4²+3²×4²=169=13²;4²+5²+4²×5²=441=21²;5²+6²+5
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 06:32:50
![找规律,并回答下列问题:已知:1²+2²+1²×2²=9=3²;2²+3²+2²×3²=49=7²;3²+4²+3²×4²=169=13²;4²+5²+4²×5²=441=21²;5²+6²+5](/uploads/image/z/11645879-23-9.jpg?t=%E6%89%BE%E8%A7%84%E5%BE%8B%2C%E5%B9%B6%E5%9B%9E%E7%AD%94%E4%B8%8B%E5%88%97%E9%97%AE%E9%A2%98%EF%BC%9A%E5%B7%B2%E7%9F%A5%EF%BC%9A1%26%23178%3B%2B2%26%23178%3B%2B1%26%23178%3B%C3%972%26%23178%3B%3D9%3D3%26%23178%3B%EF%BC%9B2%26%23178%3B%2B3%26%23178%3B%2B2%26%23178%3B%C3%973%26%23178%3B%3D49%3D7%26%23178%3B%EF%BC%9B3%26%23178%3B%2B4%26%23178%3B%2B3%26%23178%3B%C3%974%26%23178%3B%3D169%3D13%26%23178%3B%EF%BC%9B4%26%23178%3B%2B5%26%23178%3B%2B4%26%23178%3B%C3%975%26%23178%3B%3D441%3D21%26%23178%3B%EF%BC%9B5%26%23178%3B%2B6%26%23178%3B%2B5%26%231)
找规律,并回答下列问题:已知:1²+2²+1²×2²=9=3²;2²+3²+2²×3²=49=7²;3²+4²+3²×4²=169=13²;4²+5²+4²×5²=441=21²;5²+6²+5
找规律,并回答下列问题:
已知:1²+2²+1²×2²=9=3²;
2²+3²+2²×3²=49=7²;
3²+4²+3²×4²=169=13²;
4²+5²+4²×5²=441=21²;
5²+6²+5²×6²=961=31²;
100²+101²+100²×101²=( ).
一般地,有( ),并证明你的结论.
找规律,并回答下列问题:已知:1²+2²+1²×2²=9=3²;2²+3²+2²×3²=49=7²;3²+4²+3²×4²=169=13²;4²+5²+4²×5²=441=21²;5²+6²+5
100²+101²+100²×101²=( 10101² ).
一般地,有 n²+(n+1)² +n²×(n+1)²=[n×(n+1)+1]²
证明时,两边展开即可.