def fun$2($ n $)$ :

x $=0$

f o r i in range $($ n $)$ :

f o r j in range $($ n $)$ :

f o r k in range $(1,$ n $)$ :

x $=$ x $+1$

r e t u r n x Calculate T$($n$),$ making sure not to discard constants or low$-$order terms yet $($you may or may not

count the counting variable in a for loop$)$

$$ Given what you think is the Big$-$O performance for the function

$$ Prove that your proposed Big$-$O for the function is correct $($make sure to show your work; do not

just provide values for c and n$0$