阅读以下求 1+2+3+...+n 的值的过程.因为 (n+1)^2 - n^2 = 2n+1阅读以下求 1+2+3+...+n 的值的过程.因为 (n+1)^2 - n^2 = 2n+1n^2 - (n-1)^2 = 2(n-1) + 1..........2^2 - 1^2 = 2*1 + 1.以上各式相加得(n+1)^2 - 1 = 2(1+2+...+n) + n
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![阅读以下求 1+2+3+...+n 的值的过程.因为 (n+1)^2 - n^2 = 2n+1阅读以下求 1+2+3+...+n 的值的过程.因为 (n+1)^2 - n^2 = 2n+1n^2 - (n-1)^2 = 2(n-1) + 1..........2^2 - 1^2 = 2*1 + 1.以上各式相加得(n+1)^2 - 1 = 2(1+2+...+n) + n](/uploads/image/z/14698800-0-0.jpg?t=%E9%98%85%E8%AF%BB%E4%BB%A5%E4%B8%8B%E6%B1%82+1%2B2%2B3%2B...%2Bn+%E7%9A%84%E5%80%BC%E7%9A%84%E8%BF%87%E7%A8%8B.%E5%9B%A0%E4%B8%BA+%28n%2B1%29%5E2+-+n%5E2+%3D+2n%2B1%E9%98%85%E8%AF%BB%E4%BB%A5%E4%B8%8B%E6%B1%82+1%2B2%2B3%2B...%2Bn+%E7%9A%84%E5%80%BC%E7%9A%84%E8%BF%87%E7%A8%8B.%E5%9B%A0%E4%B8%BA+%28n%2B1%29%5E2+-+n%5E2+%3D+2n%2B1n%5E2+-+%28n-1%29%5E2+%3D+2%28n-1%29+%2B+1..........2%5E2+-+1%5E2+%3D+2%2A1+%2B+1.%E4%BB%A5%E4%B8%8A%E5%90%84%E5%BC%8F%E7%9B%B8%E5%8A%A0%E5%BE%97%28n%2B1%29%5E2+-+1+%3D+2%281%2B2%2B...%2Bn%29+%2B+n)
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