R - data.frame Balance calculation (use value of previous row)

Table I have:

DT <- data.frame(A=1:5*10, B=1:5*-1)
DT
   A  B
1 10 -1
2 20 -2
3 30 -3
4 40 -4
5 50 -5

Table I want:

C=A+B+C(n-1)

   A  B  C
1 10 -1  9
2 20 -2 27
3 30 -3 54
4 40 -4 90
5 50 -5 135

I have reference below link and try to apply but fail:

Use a value from the previous row in an R data.table calculation

DT$C<-DT$A+DT$B+shift(DT$C)