There was a problem similar to this a few days ago (May 27 - Find the last five digits). The same method can be used here.
Your answer is correct though you've actually made a minor mistake, the expansion begins with 1+ but that doesn't affect the hundreds digit. The actual number ends 611.
So long as you understand why it works, (high enough powers of 2010 (in this case) generate a sufficient number of zeros so that such terms don't affect the right hand end of the result), then yes it's there to use.