Pre-Algebra · Superchallenge problem

Start with the number $40$. Increase it by $\dfrac12$ of itself. Then decrease the result by $\dfrac13$ of itself. Then increase that result by $\dfrac14$ of itself, then decrease by $\dfrac15$ of itself, and so on, alternating, until the last step, which increases the current number by $\dfrac1{100}$ of itself. What is the final number?