The limit L= _ n _ i=1 ^ n 1 1+ ( b i n ) b n is equal to for some positive constant

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The limit

L=\lim_{n\to\infty}\sum_{i=1}^{n} \frac{1}{1+\left(\dfrac{b i}{n}\right)}\cdot\dfrac{b}{n}

is equal to

\ln 3

for some positive constant

b

. What is the value of

b

? (a)

e-1

(b)

3

(c)

2

(d)

\dfrac{\ln 3}{\ln 2}