Question

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

Answer 1

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