Question

已知{an}是等差数列,其n项和为Sn,S3=15,S5=35

Answer 1

(1)

S3=15=a1+a2+a3=3*a1+3*d,S5=35=a1+a2+a3+a4+a5=5*a1+10*d

那么,a1=3,d=2

an=3+2*(n-1)=2*n+1

Sn=(a1+an)*n/2=n(n+2)

(2)

bn=2/(2Sn-an+1)=1/(n^2+n)=1/n-1/(n+1)

Tn=b1+b2+……+bn=(1-1/2)+(1/2-1/3)+……+（1/n-1/(n+1)）=1-1/(n+1)=n/(n+1)