计算:12-22+32-42+52-62+72-82+92-102=_.
题目
计算:12-22+32-42+52-62+72-82+92-102=______.
答案
12-22+32-42+52-62+72-82+92-102
=-[(22-12)+(42-32)+(62-52)+(82-72)+(102-92)]
=-[(2+1)(2-1)+(4+3)+(4-3)(6+5)(6-5)+(8+7)(8-7)+(10+9)(10-9)]
=-[(2+1)×1+(4+3)×1+(6+5)×1+(8+7)×1+(10+9)×1]
=-[2+1+4+3+6+5+8+7+10+9]
=-[1+2+3+4+5+6+7+8+9+10]
=-55.
故答案为:-55.
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