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1x2+2x3+3x4+...+nx(n+1)=

因为n(n+1)=n平方+n 原式=(1平方+2平方+……n平方)+(1+2+3……n) =n(n+1)(2n+1)/6+n(n+1)/2为标准答案 注:Sn(1平方+2平方+……n平方)的证明: (a+1)³-a³=3a²+3a+1(即(a+1)³=a³+3a²+3a+1) a=1时:2³...

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6

解: s=1x2+2x3+3x4+.........nx(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+...+nx(n+1)(去括号) =1²+1+2²+2+3²+3+...+n²+n =(1²+2²+3²+...+n²)+(1+2+3+...+n) 下面的步骤可以套公式了; =n(n+1)(2n+1)...

1x2+2x3+3x4+...+nx(n+1) = n(n+1)(n+2) /3 1x2x3+2x3x4+...+n(n+1)(n+2) = n(n+1)(n+2)(n+3) /4

s=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/(n-1)-1/n) =1-1/n

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6 1x2+2x3+3x4+…+10x11 =10x(10+1)x[(10x2+1)+3]/6 =110x4 =440

一般的,有: (n-1)n(n+1) =n^3-n {n^3}求和公式:Sn=[n(n+1)/2]^2 {n}求和公式:Sn=n(n+1)/2 1x2x3+2x3x4+3x4x5+....+7x8x9 =2^3-2+3^3-3+...+8^3-8 =(2^3+3^3+...+8^3)-(2+3+...+8) =[(8*9/2)^2-1]-8*9/2+1 =1260

我小学都没毕业。俺不懂 1.M等于一,N等于负4. 其他的不懂。这些奥数题!!!!!

0x1+1x2+2x3+......+(n-1)xn =[ 1x2x(3-0)+2x3x(4-1)+......+(n-1)xnx((n+1)-(n-2)) ]/3 =( 1x2x3-0x1x2+2x3x4-1x2x3+(n-1)x(n)x(n+1)-(n-2)x(n-1)x(n) ) /3 =(n-1)n(n+1)/3 ..............中间项可以被消去 前面加上一个0x1

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