The recurrences of the form

$$T(n)=T(n-1)+f(n),\\T(0)=T_0$$ are solved by

$$T(n)=T_0+\sum_{k=1}^n f(n)$$

as you can check by induction.

(Because $T(n)=T(n-1)+f(n)=T(n-2)+f(n-1)+f(n)=T(n-3)+f(n-2)+f(n-1)+f(n)=\cdots$.)