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1×1+2×2+3×3+…1997×1997+1998×1998的个位数字是
9
9
分析:由于1~10这十个数的平方的个位数分别为1,4,9,6,5,6,9,4,1,0.以后连续自然数平方的个位数就按这个个数进行循环的.因此我们可将这十个数当成一个整体,它们的和的个位数为5.然后根据最后一个数1998进行分析计算即可.
解答:解:由于1~10这十个数的平方的个位数分别为1,4,9,6,5,6,9,4,1,0.
因此我们可将这十个数当成一个整体,它们的和为:
1+4+9+6+5+6+9+4+1+0=45,
即它们和的个位数为5.
1998÷10=199…8,
则1×1+2×2+3×3+…1997×1997+1998×1998的个位数字和是:
199×5+(1+4+9+6+5+6+9+4)
=995+44,
=1039.
即最终的个位为9.
故答案为:9.
点评:通过试算,计算出连续自然数平方个位数的排列规律,并由此进行分析是完成本题的关键.
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