document.write( "Question 39436: Evaluate the series if it converges.
\n" ); document.write( "9 + 27/4 + 81/16 + 243/64 \n" ); document.write( "
Algebra.Com's Answer #24868 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
9 + 27/4 + 81/16 + 243/64\r\n" );
document.write( "\r\n" );
document.write( "Find r by dividing every given term by the term before it\r\n" );
document.write( "\r\n" );
document.write( "27/4 divided by 9 is 3/4\r\n" );
document.write( "\r\n" );
document.write( "81/16 divided by 27/4 = 3/4\r\n" );
document.write( "\r\n" );
document.write( "243/64 divided by 81/16 = 3/4\r\n" );
document.write( "\r\n" );
document.write( "So r = 3/4\r\n" );
document.write( "\r\n" );
document.write( "This is a geometric series with |r| < 1\r\n" );
document.write( "so it converges, and we can evaluate what\r\n" );
document.write( "it converges to.  Use the formula:\r\n" );
document.write( "\r\n" );
document.write( "       a1\r\n" );
document.write( "S = 覧覧覧予r\n" );
document.write( "     1 - r \r\n" );
document.write( "\r\n" );
document.write( "a1 = 1st term = 9\r\n" );
document.write( "r = 3/4\r\n" );
document.write( "\r\n" );
document.write( "        9\r\n" );
document.write( "S = 覧覧覧覧予r\n" );
document.write( "     1 - 3/4 \r\n" );
document.write( " \r\n" );
document.write( "        9\r\n" );
document.write( "S = 覧覧覧覧予r\n" );
document.write( "       1/4\r\n" );
document.write( "\r\n" );
document.write( "S = 36\r\n" );
document.write( "\r\n" );
document.write( "So the series converges to 36, and this is called its\r\n" );
document.write( "evaluation.\r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
\n" ); document.write( "
\n" );