n / √n > [ n + 1 ] / √[n + 1]
n / √n - [ n + 1 ] / √[n + 1] > 0
n √[ n + 1] - [n + 1]√n
__________________ > 0
√n * √[n + 1]
n √[n + 1] - [n + 1]√n > 0
n √[n + 1] > [ n + 1]√n square both sides
n^2 [ n + 1] > [n + 1]^2 * n
n^2 [ n + 1] - [n + 1]^2*n > 0
n [n + 1] [ n - (n + 1 ) ] > 0
n (n + 1] [ - 1] > 0
n ( n + 1) < 0
This is only true on -1 < n < 0
So....no poistive integers make this true
Also.....see the graph here : https://www.desmos.com/calculator/tmsohselsc
Q(n) is never greater than Q(n + 1)