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Answer: 9046

 

First 2011 digits of 1.818181...
Each pair adds up to 9
There are 2011$\div$2 = 1005 remainder 1 pairs

Sum = 1005$\times$9 + 1 (from ...18...)
        = 9046


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.