I'm learning about asymptotics and time complexity.The algorithm I'm analyzing has a for loop that starts at $i = 1$ and ends at $\left \lfloor \sqrt n \right \rfloor$. The body is said to run in $n-i$ steps. I'm trying to do a summation from $i=1$ to $\left \lfloor \sqrt n \right \rfloor$ to come up with a Big Theta, but I am not sure how to deal with the upper bound of the summation. Thank you in advance. 
Summation with floor in upper bound
time complexity;asymptotics;runtime analysis