1立方+2立方+3立方+……+n的立方

S=1^3+2^3+3^3+4^3+5^3+.....=1+8+27+64+125+.....第1階差=7,19,37,61,....d1=7第2階差=12,18,24,......d2=12第3階差=6,6,6,.........d3=6公式: S=n/1!+n(n-1)d1/2!+n(n-1)(n-2)d2/3!+n(n-1)(n-2)(n-3)d3/4!=n+n(n-1)7/2+n(n-1)(n-2)12/6+n(n-1)(n-2)(n-3)6/24=n{1+7(n-1)/2+2(n^2-3n+2)+(n^3-6n^2+11n-6)/4}=n/4*{4+14(n-1)+8(n^2-3n+2)+n^3-6n^2+11n-6}=n/4*[14n-10+8n^2-24n+16+n^3-6n^2+11n-6]=n/4*[n^3+2n^2+n]=n^2/4*(n^2+2n+1)=[n(n+1)/2]^2................ans

2012-06-03 07:47:04 補充：
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