document.write( "Question 1066672: Compute the sum
\n" ); document.write( "{1}/{sqrt{100} + sqrt{102}} + {1}/{sqrt{102} + sqrt{104}} + {1}/{sqrt{104}+sqrt{106}} + ...+ {1}/{sqrt{9998} + sqrt{10000}}.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #681883 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( " = multiply the numerator and denominator by  (rationalizing the denominator) to get = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Do it with every atom in your long molecule.\r\n" );
document.write( "\r\n" );
document.write( "Then add.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Everything inside will cancel.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Only two terms survive: very first and very last.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the sum is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " -  =  = -5 - (-50) = 45.\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" );