Recurrence for recursive insertion sort
According to the description you provided the recurrence is correct.
you might think it should be
 T(n)=\begin{Bmatrix}
1 &amp; ,\ n=1\\ 
T(n-1)\ +\ \Theta(log\ n) &amp; ,\ otherwise 
\end{Bmatrix}

because you can find the insertion place by using Binary-Search, however in order to actually insert the element you'll have to move away all the elements in the worst case.