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1×1-2×2+3×3-4×4+5×5-6×6+…-100×100+101×101.
分析:通过观察,此题应从后向前计算,用平方差公式a2-b2=(a+b)×(a-b),很快得出结果.
解答:解:1×1-2×2+3×3-4×4+5×5-6×6+…-100×100+101×101,
=1012-1002+…+32-22+1,
=(101-100)×(101+100)+…+(3-2)×(3+2)+1,
=101+100+99+98+…+2+1,
=(101+1)×101÷2,
=5151.
点评:此题考查了平方差公式a2-b2=(a+b)×(a-b).
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