100²-99²-98²-97²…-4²-3²-2²
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:综合作业 时间:2024/08/18 16:37:08
100²-99²-98²-97²…-4²-3²-2²-1²
![100²-99²-98²-97²…-4²-3²-2²](/uploads/image/z/17653706-26-6.jpg?t=100%26%23178%3B%EF%BC%8D99%26%23178%3B%EF%BC%8D98%26%23178%3B%EF%BC%8D97%26%23178%3B%E2%80%A6%EF%BC%8D4%26%23178%3B%EF%BC%8D3%26%23178%3B%EF%BC%8D2%26%23178)
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 + 97 +...+ 4 + 3 + 2 + 1
= (100 + 1) + (99 + 2) + ...+(51 + 50)
= 101×50
= 5050
= (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 + 97 +...+ 4 + 3 + 2 + 1
= (100 + 1) + (99 + 2) + ...+(51 + 50)
= 101×50
= 5050
一、100²-99²+98²-97²+96²-95²+……+
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