100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 07:14:45
![100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²](/uploads/image/z/1239918-6-8.jpg?t=100%26%23178%3B-99%26%23178%3B%2B98%26%23178%3B-97%26%23178%3B%2B96%26%23178%3B-95%26%23178%3B%2B96%26%23178%3B-95%26%23178%3B%2B%C2%B7%C2%B7%C2%B7%2B2%26%23178%3B-1%26%23178%3B)
100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²
100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²
100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²
100²-99²+98²-97²+96²-95²+96²-95²+···+2²-1²?
应该是100²-99²+98²-97²+96²-95²+94²-93²+···+2²-1² 吧?
如果是的话:
100²-99²+98²-97²+96²-95²+94²-93²+···+2²-1²
=(100-99)(100+99)+(98-97)(98+97)+(96-95)(96+95)+(94²-93)(94+93)+···+(2-1)(2+1)
=100+99+98+97+96+95+94+93+……+2+1
=(100+1)×100÷2
=10100÷2
=5050