数列题一道,已知数列an中,a1=3,前n项和为Sn=1/2(n+1)(an+1)-1.(1)求证:数列an是等差数列(2)求数列an的通项公式(3)设数列2/an*a(n-1)的前n项和为Tn,问是否存在实数M,使得Tn

Question

数列题一道,
已知数列an中,a1=3,前n项和为Sn=1/2(n+1)(an+1)-1.
(1)求证:数列an是等差数列
(2)求数列an的通项公式
(3)设数列2/an*a(n-1)的前n项和为Tn,问是否存在实数M,使得Tn

Answer 1

1 n=(n+1)(an+1)/2-1 S(n-1)=n*[a(n-1)+1]/2-1 an=Sn-S(n-1)=[nan+1+an+n-na(n-1)-n]/2 2an=(n+1)an-n(n-1)+1 (n-1)an=na(n-1)+1 an/n=a(n-1)/(n-1)+1/n*(n-1)=a(n-1)/(n-1)+1/(n-1)-1/n an/n+1/n=a(n-1)/(n-1)+1/(n...