MathDB

Let

C: y=\ln x

. For each positive integer

n

, denote by

A_n

the area of the part enclosed by the line passing through two points

(n,\ \ln n),\ (n+1,\ \ln (n+1))

and denote by

B_n

that of the part enclosed by the tangent line at the point

(n,\ \ln n)

C

and the line

x=n+1

. Let

g(x)=\ln (x+1)-\ln x

.
(1) Express

A_n,\ B_n

in terms of

n,\ g(n)

respectively.
(2) Find

\lim_{n\to\infty} n\{1-ng(n)\}

Problem Statement