(1)Use the binomial theorem to find the 18th term in the binomial expansion of [2m-n(sqrt(2)]^27
\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Usually the letter n is used to represent a general number, not a specific\r\n" );
document.write( "number, but here n is used as a specific number, so I can't speak of the \"nth\r\n" );
document.write( "term\", so I'll have to speak of the \"pth\" term instead to avoid conflict of\r\n" );
document.write( "letters.\r\n" );
document.write( "\r\n" );
document.write( "The pth term of 
, if you start counting with 0 instead of 1, is\r\n" );
document.write( "\r\n" );
document.write( "
, \r\n" );
document.write( "\r\n" );
document.write( "where 
is the binomial coefficient which is the same as\r\n" );
document.write( "C(s,p) or sCp or \"the number of combinations of s things taken p at a time.\"\r\n" );
document.write( "\r\n" );
document.write( "The 18th term is the 17th term if we start counting from 0, so we\r\n" );
document.write( "substitute \r\n" );
document.write( "\r\n" );
document.write( "
, 
, 
, 
\r\n" );
document.write( "\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "
and simplify a little:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Further simplifying the factors separately:\r\n" );
document.write( " 
= 
<-- using a TI-84 calculator\r\n" );
document.write( " 
= 
= 
\r\n" );
document.write( " 
= 
\r\n" );
document.write( " 
= 
= 
= 
= 
= 
= 
\r\n" );
document.write( "\r\n" );
document.write( "Putting them all together:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
<-- answer\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------\r\n" );
document.write( "
\n" );
document.write( "(2)Find the 69th number in the 72nd row (n=72) of Pascal’s triangle.
\n" );
document.write( "\r\n" );
document.write( "Again we start counting from 0, so the 69th number starting counting with 1,\r\n" );
document.write( "is the 68th number, when we start counting with 0 instead of 1. \r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "If you can't use a calculator you can use \r\n" );
document.write( "\r\n" );
document.write( "
.\r\n" );
document.write( "\r\n" );
document.write( " <-- answer\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-12.gif\")
