Bubbles

The picture shows how this works with the string "ant".

The length of "ant" is

1 + (the length of "nt")

1 + (1 + the length of "t")

1 + (1 + (1 + the length of ""))

= 1 + (1 + (1 + 0))

= 1 + (1 + (1))

= 1 + 2

= 3

Sometimes recursion seems backwards. The last "1" added to the sum is for the first character of the string. Look at the bottom bubble of the diagram. If you start with it and go upwards, it is like counting characters 0, 1, 2, 3 from the end of the string to the first character.