利用因式分解计算:1-2²+3²-4²+5²-6²+···+99²-100²+101²
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 01:39:32
![利用因式分解计算:1-2²+3²-4²+5²-6²+···+99²-100²+101²](/uploads/image/z/626141-29-1.jpg?t=%E5%88%A9%E7%94%A8%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E8%AE%A1%E7%AE%97%3A1-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B5%26%23178%3B-6%26%23178%3B%2B%C2%B7%C2%B7%C2%B7%2B99%26%23178%3B-100%26%23178%3B%2B101%26%23178%3B)
利用因式分解计算:1-2²+3²-4²+5²-6²+···+99²-100²+101²
利用因式分解计算:1-2²+3²-4²+5²-6²+···+99²-100²+101²
利用因式分解计算:1-2²+3²-4²+5²-6²+···+99²-100²+101²
1-2²+3²-4²+5²-6²+···+99²-100²+101²
=(101²-100²)+(99²-98²)+……+(3²-2²)+1
=(101+100)×(101-100)+(99+98)×(99-98)+……(3+2)×(3-2)+1
=201+197+……+5+1
=(201+1)+(197+5)+(193+9)+……
=202+202+202+……
=202×[(201+3)÷8]
=202×25.5
=5151