document.write( "Question 773085: 3+33+333+3333+......+333333333333 in this addition which digit is there at the hundreds place \n" ); document.write( "
Algebra.Com's Answer #471303 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "3+33+333+3333+......+333333333333\r\n" );
document.write( "\r\n" );
document.write( "The 1st term has 1 3, the 2nd term has 2 3's, the 3rd term has 3 3's, etc\r\n" );
document.write( "The last term has 12 3's, so there are 12 terms.\r\n" );
document.write( "\r\n" );
document.write( "The last three digits will be the same as if we just added the \r\n" );
document.write( "first two terms which have no hundreds digit, and then added 333 \r\n" );
document.write( "ten times: \r\n" );
document.write( "\r\n" );
document.write( "3 + 33 + 333 + 333 + 333 + ... + 333 where there are 10 333's\r\n" );
document.write( "\r\n" );
document.write( "3 + 33 + 10*333 = 3366\r\n" );
document.write( "\r\n" );
document.write( "So the hundreds digit will be 3.\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "If we did it the long way, we'd have:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "           3   \r\n" );
document.write( "          33                                                      \r\n" );
document.write( "         333    \r\n" );
document.write( "        3333      \r\n" );
document.write( "       33333                                                      \r\n" );
document.write( "      333333  \r\n" );
document.write( "     3333333                                                   \r\n" );
document.write( "    33333333   \r\n" );
document.write( "   333333333\r\n" );
document.write( "  3333333333                                                   \r\n" );
document.write( " 33333333333                            \r\n" );
document.write( "333333333333\r\n" );
document.write( "------------\r\n" );
document.write( "370370370366\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );