Here you have 10 terms due to the bearing rate change (from 0.01 to 0.1). However, if you assume stepwise increments, there should be 9 terms with the last one being 0.09. Indeed, in your calculation in the previous quote, for time +1 the rate change did not make a contribution, for time +2 the contribution was 0.01, for time +3 it was 0.01 + 0.02.

If we assume that the bearing rate, which I denoted

, changes continuously, let's see how it depends on time.

Initially it is

and then it grows linearly with

, so at time

it becomes

. The actual bearing is the shaded area under the graph (e.g., when

, it is just

). The triangle area is

(half of a rectangle with sides

and

), so the shaded area is

. Therefore, the bearing at time

is

.

If you insist on stepwise increment to the bearing rate, then you can use

the formula for the sum of arithmetic progression:

when

is an integer and

. Then the bearing at time

is

.