3+33+333+3333+......+333333333333

The 1st term has 1 3, the 2nd term has 2 3's, the 3rd term has 3 3's, etc
The last term has 12 3's, so there are 12 terms.

The last three digits will be the same as if we just added the 
first two terms which have no hundreds digit, and then added 333 
ten times: 

3 + 33 + 333 + 333 + 333 + ... + 333 where there are 10 333's

3 + 33 + 10*333 = 3366

So the hundreds digit will be 3.

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If we did it the long way, we'd have:

 
           3   
          33                                                      
         333    
        3333      
       33333                                                      
      333333  
     3333333                                                   
    33333333   
   333333333
  3333333333                                                   
 33333333333                            
333333333333
------------
370370370366

Edwin