数列{an}中,a1=2,an+1(n+1为下标)=an+ln(1+1/n)则an=?

数列{an}中,a1=2,an+1(n+1为下标)=an+ln(1+1/n)则an=?
数列{an}中,a1=2,an+1(n+1为下标)=an+ln(1+1/n)则an=?

数列{an}中,a1=2,an+1(n+1为下标)=an+ln(1+1/n)则an=?
an - a(n-1)= ln n/(n-1)
a(n-1) - a(n-2) = ln (n-1)/(n-2)
……
a2 - a1 = ln2/1
左右相加
an-a(n-1)+a(n-1) -……-a1 = ln (1+n)/n + ln n/(n-1)+……ln 2/1 = ln (1+n)/n * … 2/1 = ln n
an = 2+ln n