用因式分解解下列各式:100²-99²+98²-97²+96²-95²+...+2²-1
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 04:00:47
![用因式分解解下列各式:100²-99²+98²-97²+96²-95²+...+2²-1](/uploads/image/z/745070-14-0.jpg?t=%E7%94%A8%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E8%A7%A3%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%3A100%26%23178%3B-99%26%23178%3B%2B98%26%23178%3B-97%26%23178%3B%2B96%26%23178%3B-95%26%23178%3B%2B...%2B2%26%23178%3B-1)
用因式分解解下列各式:100²-99²+98²-97²+96²-95²+...+2²-1
用因式分解解下列各式:100²-99²+98²-97²+96²-95²+...+2²-1
用因式分解解下列各式:100²-99²+98²-97²+96²-95²+...+2²-1
100²-99²+98²-97²+96²-95²+...+2²-1
=(100²-99²)+(98²-97²)+(96²-95²)+...+(2²-1)
=(100+99)(100-99)+(98+97)(98-97)+(96+95)(96-95)+……+(2+1)(2-1)
=100+99+98+97+96+95+……+2+1
=(100+1)×100÷2
=5050