Limits + Integration + Summation!
Calculus
Level
5
We denote the two functions \( f(x) = \lfloor x \rfloor - x \) and \(\displaystyle g(x) = \lim_{n\to\infty} \frac{(f(x))^{4n}-1}{(f(x))^{4n}+1} \).
Find the value of \( \displaystyle \int \sum_{r=1}^{2014} (g(x))^r \, dx \).
by
Nishant Rai