As I said in previous post the formal definition of the Riemann Integral is very useful when solving Olympiad problems.
Problem 1. Find the following limit
Solution. Let try to make our sum into something more or less similar to Riemann sum.
Does this remind you of the monstrous ? But what if set and consider the right Riemann sum? Now it will transform into .
From the last formula we can easily understand what function we need to consider, so by the definition:
Now using the same approach try solving the following problems.