document.write( "Question 1088714: If the coefficients of (m+1)th term and the (m+3)th term in the expansion of (1+x)^20 are equal then the value of m is-:
\n" ); document.write( "a)10
\n" ); document.write( "b)9
\n" ); document.write( "c)8
\n" ); document.write( "d)7 \n" ); document.write( "

Algebra.Com's Answer #703015 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "20C(m+1) = 20C(m+3)\r\n" );
document.write( "\r\n" );
document.write( "If we knew enough about the symmetry of Pascal's triangle we'd\r\n" );
document.write( "know that the middle term would have coefficient 20C10 and therefore\r\n" );
document.write( "10 would have to be halfway between m+1 and m+3, so 10 would be\r\n" );
document.write( "their average\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "However, we'll do it assuming we didn't know that much about Pascal's\r\n" );
document.write( "triangle.  We use the definition of combinations:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Numerators are equal so denominators must also be equal:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by (m+1)!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by (17-m)!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"FOIL\" out both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );