1.已知1×4+2×7+3×10+...n(3n+1)=n(n+1)^2,不用数学归纳法,证明对於所有正整数n,1^2+2^2+3^2+...n^2=n(n+1)(2n+1)/62.设y = xln(2-x).(a)从基本原理求dy/dx.(b)若y = xln(2-x)在x=1的切线垂直於直线x+ky+3=0,求k的值.
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![1.已知1×4+2×7+3×10+...n(3n+1)=n(n+1)^2,不用数学归纳法,证明对於所有正整数n,1^2+2^2+3^2+...n^2=n(n+1)(2n+1)/62.设y = xln(2-x).(a)从基本原理求dy/dx.(b)若y = xln(2-x)在x=1的切线垂直於直线x+ky+3=0,求k的值.](/uploads/image/z/11376852-60-2.jpg?t=1.%E5%B7%B2%E7%9F%A51%C3%974%EF%BC%8B2%C3%977%EF%BC%8B3%C3%9710%EF%BC%8B...n%283n%EF%BC%8B1%29%3Dn%28n%2B1%29%5E2%2C%E4%B8%8D%E7%94%A8%E6%95%B0%E5%AD%A6%E5%BD%92%E7%BA%B3%E6%B3%95%2C%E8%AF%81%E6%98%8E%E5%AF%B9%E6%96%BC%E6%89%80%E6%9C%89%E6%AD%A3%E6%95%B4%E6%95%B0n%2C1%5E2%2B2%5E2%2B3%5E2%2B...n%5E2%3Dn%28n%2B1%29%282n%2B1%29%2F62.%E8%AE%BEy+%3D+xln%282-x%29.%28a%29%E4%BB%8E%E5%9F%BA%E6%9C%AC%E5%8E%9F%E7%90%86%E6%B1%82dy%2Fdx.%28b%29%E8%8B%A5y+%3D+xln%282-x%29%E5%9C%A8x%3D1%E7%9A%84%E5%88%87%E7%BA%BF%E5%9E%82%E7%9B%B4%E6%96%BC%E7%9B%B4%E7%BA%BFx%2Bky%2B3%3D0%2C%E6%B1%82k%E7%9A%84%E5%80%BC.)
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