已知等差数列的前n项和为a,前2n项和为b,求前3n项和
问题描述：
已知等差数列的前n项和为a,前2n项和为b,求前3n项和
答
c(n) = c + (n-1)d,n=1,2,...a = S(n) = nc + n(n-1)d/2,b = S(2n) = 2nc + n(2n-1)d,b - 2a = n(2n-1)d - n(n-1)d = n^2d,d = (b-2a)/n^2,c = a/n - (n-1)d/2 = a/n - (n-1)(b-2a)/[2n^2]S(3n) = 3nc + 3n(3n-1)d/2...