数列an满足a1=1/2,a1+a2+a3……an=n^2an,则an
问题描述:
数列an满足a1=1/2,a1+a2+a3……an=n^2an,则an
答
an=1/[(n+1)*n]
答
an=1/(n^2+n)
答
n^2an是n的2次方乘以数列的第n项an吗?如果是,可以用递推公式表述:
A1=1/2,An=[(n-1)^2]An-1 /[n^2-1].
答
a1+a2+a3……a(n+1)=(n+1)^2an+1=n²an+a(n+1)得
(n+2)*a(n+1)=n*an即a(n+1)/an=n/(n+2)最后累乘得an=1/[(n+1)*n]
答
s(n)=n^2a(n)a(n+1)=s(n+1)-s(n)=(n+1)^2a(n+1)-n^2a(n)n(n+2)a(n+1)=n^2a(n)(n+2)a(n+1)=na(n)(n+2)(n+1)a(n+1)=(n+1)na(n)(n+2)(n+1)a(n+1)=(n+1)na(n)=...=(1+1)*1*a(1)=1a(n)=1/[n(n+1)] = 1/n - 1/(n+1)