对于任意正整数n,都有a1+a2+..+an=n^3 则lim(1/(a2-1)+1/(a3-1)+.1(an-1) )=对于任意_数学解答

对于任意正整数n,都有a1+a2+..+an=n^3 则lim(1/(a2-1)+1/(a3-1)+.1(an-1) )=
对于任意正整数n,都有a1+a2+..+an=n^3 则lim(1/(a2-1)+1/(a3-1)+.1(an-1) )= 求出AN的通项然后则么做

人气：265 ℃　时间：2020-05-08 01:22:11

解答

a1+a2+..+an=n^3 (1)a1+a2+..+an+a(n+1)=(n+1)^3 (2)由（2)-(1)得,a（n+1)=3n^2+3n+1=3n(n+1)+1即an=3(n-1)n+1所以,1/(an-1)=1/3n(n-1)=1/3[1/(n-1)-1/n]lim(1/(a2-1)+1/(a3-1)+.1(an-1) )=1/3{(1-1/2)+1/2-1/3.(1/(...