10.在数列{an}中,a1=2,an+1=an+ln(1+1/n),则an=()A.2+ln n B.2+(n-1)ln n C.2+nln n D.1+n+ln n

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10.在数列{an}中,a1=2,an+1=an+ln(1+1/n),则an=()A.2+ln n B.2+(n-1)ln n C.2+nln n D.1+n+ln n
10.在数列{an}中,a1=2,an+1=an+ln(1+1/n),则an=()
A.2+ln n B.2+(n-1)ln n
C.2+nln n D.1+n+ln n

10.在数列{an}中,a1=2,an+1=an+ln(1+1/n),则an=()A.2+ln n B.2+(n-1)ln n C.2+nln n D.1+n+ln n
A(n+1)-An=ln((n+1)/n)
依此类推
An-A(n-1)=ln(n/(n-1))
A(n-1)-A(n-2)=ln((n-1)/(n-2))
……
A2-A1=ln(2/1)
上式相加
An-A1=ln(n/(n-1)+ln((n-1)/(n-2))+……+ln(2/1)
=ln[(n/(n-1)×((n-1)/(n-2))×……×(2/1)]
=ln(n)
An=A1+ln(n)=2+ln(n)
选A