等差数列前n项立方和公式（等差数列前n项立方和公式有哪些）

a(n)=a(1)+(n-1)d[a(n)]^3=[a(1)+(n-1)d]^3=[a(1)]^3+3(n-1)d[a(1)]^2+3(n-1)^2d^2 a(1)+(n-1)^3d^3，我来为大家讲解一下关于等差数列前n项立方和公式?跟着小编一起来看一看吧!

等差数列前n项立方和公式

a(n)=a(1)+(n-1)d

[a(n)]^3=[a(1)+(n-1)d]^3=[a(1)]^3+3(n-1)d[a(1)]^2+3(n-1)^2d^2 a(1)+(n-1)^3d^3

[a[1]]^3+a[2]^3+...........+a[n]^3

=n[a(1)]^3

+3d[a(1)]^2 [0+1+2+.......(n-1)]

+3d^2 a(1) [0^2+1^2+...........+(n-1)^2]

+d^3 [0^3+1^3+........+(n-1)^3]

=n[a(1)]^3+3d[a[1]]^2 n(n-1)/2+ n[a(1)]^3*(n-1)n(2n-1)/2+d^3*n^2(n-1)^2/4