为什么3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)这样算3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)为什么3×(1×2+2×3+3×4+...+99×100) 会等于99x100x101
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![为什么3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)这样算3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)为什么3×(1×2+2×3+3×4+...+99×100) 会等于99x100x101](/uploads/image/z/53794-10-4.jpg?t=%E4%B8%BA%E4%BB%80%E4%B9%883%C3%97%EF%BC%881%C3%972%2B2%C3%973%2B3%C3%974%2B...%2B99%C3%97100%EF%BC%89%3D%EF%BC%8899%EF%BC%89%C3%97%EF%BC%88100%EF%BC%89%C3%97%EF%BC%88101%EF%BC%89%E8%BF%99%E6%A0%B7%E7%AE%973%C3%97%EF%BC%881%C3%972%2B2%C3%973%2B3%C3%974%2B...%2B99%C3%97100%EF%BC%89%3D%EF%BC%8899%EF%BC%89%C3%97%EF%BC%88100%EF%BC%89%C3%97%EF%BC%88101%EF%BC%89%E4%B8%BA%E4%BB%80%E4%B9%883%C3%97%EF%BC%881%C3%972%2B2%C3%973%2B3%C3%974%2B...%2B99%C3%97100%EF%BC%89+%E4%BC%9A%E7%AD%89%E4%BA%8E99x100x101)
为什么3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)这样算3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)为什么3×(1×2+2×3+3×4+...+99×100) 会等于99x100x101
为什么3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)这样算
3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)
为什么3×(1×2+2×3+3×4+...+99×100) 会等于99x100x101
为什么3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)这样算3×(1×2+2×3+3×4+...+99×100)=(99)×(100)×(101)为什么3×(1×2+2×3+3×4+...+99×100) 会等于99x100x101
原式=3×(1×1+2×2+3×3+...+99×99+1+2+3……+99)
=3×(1^2+2^2+3^2+…+99^2)+3×(1+2+3……+99)
=3×99×100×199×1/6+3×100×99×1/2
=(199/2+3/2)×99×100
=99×100×101
【1^2+2^2+3^2+…+n^2=n(n+1)(2n+1)/6 (注:N^2=N的平方) 】
【1+2+3……+n=(1+n)n/2】
祝你新年快乐!
因为:
1×2=1/3×(1×2×3-0×1×2)
2×3=1/3×(2×3×4-1×2×3)
3×4=1/3×(3×4×5-2×3×4)
……
99×100=1/3×(99×100×101-98×99×100)
1×2+2×3+3×4+...+99×100
=1/3×(1×2×3-0×1×2)+1/3×(2×3×4-1×2×3)+……+1/...
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因为:
1×2=1/3×(1×2×3-0×1×2)
2×3=1/3×(2×3×4-1×2×3)
3×4=1/3×(3×4×5-2×3×4)
……
99×100=1/3×(99×100×101-98×99×100)
1×2+2×3+3×4+...+99×100
=1/3×(1×2×3-0×1×2)+1/3×(2×3×4-1×2×3)+……+1/3×(99×100×101-98×99×100)
=1/3×99×100×101
所以:3×(1×2+2×3+3×4+...+99×100)
=3×1/3×99×100×101
=99×100×101
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晕死,数学黑洞