1²-2²+3²-4²+...+9²-10²等于多少(简便方法计算)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 23:15:55
![1²-2²+3²-4²+...+9²-10²等于多少(简便方法计算)](/uploads/image/z/132108-60-8.jpg?t=1%26%23178%3B-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B...%2B9%26%23178%3B-10%26%23178%3B%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%EF%BC%88%E7%AE%80%E4%BE%BF%E6%96%B9%E6%B3%95%E8%AE%A1%E7%AE%97%EF%BC%89)
1²-2²+3²-4²+...+9²-10²等于多少(简便方法计算)
1²-2²+3²-4²+...+9²-10²等于多少(简便方法计算)
1²-2²+3²-4²+...+9²-10²等于多少(简便方法计算)
解
利用平方差公式
原式
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+……+(9-10)(9+10)
=-(1+2)-(3+4)-……-(9+10)
=-(1+2+3+4+…+9+10)
=-(1+10)×10÷2
=-55