Question

If [x] denotes the integral part of x, then find

Answer 1

hint :
1^2x-1<[1^2x]<=1^2x
2^2x-1<[2^2x]<=2^2x
..
n^2x-1<[n^2x]<=n^2x
now sum of them
then use sandwich theroem

Answer 2

can we take x common from the numerator,