Sum of $n$ factorials: The following function sum$\_$fact$($num$),$ attempts to calculate the sum of factorials of all the numbers from $1$ to $n.$ For example sum$\_$fact $(5)=1!+2!+3!+4!+5153$

Identify and correct the errors in the following function:

def sum$\_$fact $(n)$ :

sum $=0$

for $i$ in range $1,n+1$ :

fact $=0$

for j in r$$nge $1,n+1$ :

fact $**=j$

sum $+=$ fact

return sum