Mathematics problem

Question

I have this limit problem. I have tried to attempt it. Here is my attempt. But my answer is not matching with the book, please help.

Note: Greatest integer function is same as floor function.

Answer 1

Fascinating problem!

Think the "floor" of all even powers of x≈0^- is zero? So the sum equals (-1) × (n+1), the numerator vanishes, and the limit is itself zero?