Question 190
Which number is larger, $A$ or $B$, where
$$
A=\frac{1}{2015}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2015}\right) \quad \text{and} \quad B=\frac{1}{2016}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2016}\right) ?
$$
Prove that your answer is correct.
$$
A=\frac{1}{2015}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2015}\right) \quad \text{and} \quad B=\frac{1}{2016}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2016}\right) ?
$$
Prove that your answer is correct.