Question 97
Prove that
$$
\log_2 \left(1 + \frac{1}{1}\right) + \log_2 \left(1 + \frac{1}{2}\right) + \dots + \log_2 \left(1 + \frac{1}{k}\right) + \dots + \log_2 \left(1 + \frac{1}{2014}\right) \lt 11.
$$
$$
\log_2 \left(1 + \frac{1}{1}\right) + \log_2 \left(1 + \frac{1}{2}\right) + \dots + \log_2 \left(1 + \frac{1}{k}\right) + \dots + \log_2 \left(1 + \frac{1}{2014}\right) \lt 11.
$$