怎么算这个啊100²-99²+98²+97²···+4²-3²+2²-1²
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 12:02:34
![怎么算这个啊100²-99²+98²+97²···+4²-3²+2²-1²](/uploads/image/z/5298375-39-5.jpg?t=%E6%80%8E%E4%B9%88%E7%AE%97%E8%BF%99%E4%B8%AA%E5%95%8A100%26%23178%3B-99%26%23178%3B%2B98%26%23178%3B%2B97%26%23178%3B%C2%B7%C2%B7%C2%B7%2B4%26%23178%3B-3%26%23178%3B%2B2%26%23178%3B-1%26%23178%3B)
怎么算这个啊100²-99²+98²+97²···+4²-3²+2²-1²
怎么算这个啊100²-99²+98²+97²···+4²-3²+2²-1²
怎么算这个啊100²-99²+98²+97²···+4²-3²+2²-1²
100²-99²+98²+97²···+4²-3²+2²-1²
=(100+99)(100-99)+(98+97)(98-97)+.+(4+3)(4-3)+(2+1)(2-1)
=100+99+98+.+4+3+2+1
=(100+1)*100/2
=5050
98的平方后面是加还是减?
100²-99²+98²+97²···+4²-3²+2²-1²
=(100-99)(100+99)+(98-97)(98+97)+(96-95)(96+95)+-----+(4-3)(4+3)+(2-1)(2+1)
=199+195+191+187+-----+7+3
=(199+3)x50/2
=5050