Let's indicate with the limit...
... where is the so called 'floor function'. On the basis of geometrical considerations [a diagram would be useful to better undestand...] you can demonstrate that is...
... so that...
Kind regards
Define . Prove that exists and .
Attempt
My issue is the integral in the sequence. I don't know how to take the limit of the sequence with that in there. I think there is a way to break up the integral to take the limit of the sequence easier. I need help with this question. Thanks in advance.