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:2024/08/15 09:34:12
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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