document.write( "Question 1081650: (1+1/2)(1+1/4)(1+1/16)(1+1/256)......... \n" ); document.write( "
Algebra.Com's Answer #695727 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "(1+1/2)(1+1/4)(1+1/16)(1+1/256).........
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let P = \"%281%2B1%2F2%29%281%2B1%2F4%29%281%2B1%2F16%29%281%2B1%2F256%29+ellipsis\".\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"1-1%2F2\"  (which is \"1%2F2\", of course).\r\n" );
document.write( "\r\n" );
document.write( "Use\r\n" );
document.write( "\r\n" );
document.write( "\"%281-1%2F2%29%2A%281%2B1%2F2%29\" = \"1-1%2F4\",\r\n" );
document.write( "\r\n" );
document.write( "\"%281-1%2F4%29%2A%281%2B1%2F4%29\" = \"1-1%2F16\",\r\n" );
document.write( "\r\n" );
document.write( "\"%281-1%2F16%29%2A%281%2B1%2F16%29\" = \"1-1%2F256\",\r\n" );
document.write( "\r\n" );
document.write( "and so on INFINITELY MANY times . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You will get \"%281%2F2%29%2AP\" = 1,   which implies  P = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  P = 2.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );