为什么3[6x+6(x-1)+6(x-2)+6(x-3)+.6x2+6x1]=9x(x+1)?

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为什么3[6x+6(x-1)+6(x-2)+6(x-3)+.6x2+6x1]=9x(x+1)?

为什么3[6x+6(x-1)+6(x-2)+6(x-3)+.6x2+6x1]=9x(x+1)?
为什么3[6x+6(x-1)+6(x-2)+6(x-3)+.6x2+6x1]=9x(x+1)?

为什么3[6x+6(x-1)+6(x-2)+6(x-3)+.6x2+6x1]=9x(x+1)?
根据等差数列求和公式:
x+(x-1)+(x-2)+……+2+1=x(x+1)/2
那么,两边都乘以6,同时对左边用乘法分配律,就有:
6x+6(x-1)+6(x-2)+……+6×2+6×1=3x(x+1)
再使两边都乘以3,就得到了原式:
3[6x+6(x-1)+6(x-2)+……+6×2+6×1]=9x(x+1)

18(x*x-(1+2+...+x-1))=18[(x^2)-x(x-1)/2]=18[x^2+x/2]=9(x^2+x)=9x(x+1)

学过等差数列不1+2+3+、、、+x=(1+x)x/2再用这个式子乘18就出来了

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