已知数列{an}的通项公式an=6n-5,设bn=1/an*an+1,Tn是数列{bn}的前n项和,求Tn_数学解答

已知数列{an}的通项公式an=6n-5,设bn=1/an*an+1,Tn是数列{bn}的前n项和,求Tn

人气：326 ℃　时间：2019-12-20 18:22:00

解答

a(n)*a(n+1)=(6n-5)(6n+1)
1/[(6n-5)(6n+1)=(1/6)*[1/(6n-5)-1/(6n+1)]
Tn=(1/6)*[1-1/7+1/7-1/13+1/13-1/19+...+1/(6n-5)-1/(6n+1)]
=(1/6)*[1-1/(6n+1)]