Question

在數(shù)列{an}中,a1=2,an+1=an+ln(1+),則an=(　　)

(A)2+lnn(B)2+(n-1)lnn(C)2+nlnn(D)1+n+lnn

 

Answer 1

A

【解析】【思路點(diǎn)撥】根據(jù)遞推式采用“疊加”方法求解.

解:∵an+1=an+ln(1+)=an+ln=an+ln(n+1)-lnn,

∴a2=a1+ln2,a3=a2+ln3-ln2,…,an=an-1+lnn-ln(n-1),

將上面n-1個(gè)式子左右兩邊分別相加得an=a1+ln2+(ln3-ln2)+(ln4-ln3)+…+[lnn-ln(n-1)]=a1+lnn=2+lnn.