document.write( "Question 249859: For the expansion of (k+t)^22 ,state
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Algebra.Com's Answer #186468 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The binomial expansion is easier if you don't call the first\r\n" );
document.write( "term \"the first term\" but instead call it \"the zero-th term\",\r\n" );
document.write( "and call the second term \"the first term\" and then call the last\r\n" );
document.write( "term the nth term, (which is really the (n+1)st term).\r\n" );
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document.write( "If you use that \"start counting from 0 instead of 1\" convention \r\n" );
document.write( "then the Rth term of \r\n" );
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document.write( "is  which is sometimes written  and sometimes\r\n" );
document.write( "written  but it always means , \r\n" );
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document.write( "the 0th term's coefficient is  or  or \r\n" );
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document.write( "which means \r\n" );
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document.write( "The 1st term's coefficient is  or  or \r\n" );
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document.write( "which means  \r\n" );
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document.write( "=  =\r\n" );
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document.write( "=  =\r\n" );
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document.write( "The 2nd term's coefficient is  or  or \r\n" );
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document.write( "which means  \r\n" );
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document.write( "=  =\r\n" );
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document.write( "=  =\r\n" );
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document.write( "You can also just skip all that cancelling and observe\r\n" );
document.write( "the pattern of what's always left after cancelling:\r\n" );
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document.write( "If you needed the 3rd term's coefficient (really the 4th term's), \r\n" );
document.write( "it would be\r\n" );
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document.write( "If you needed the 4th term's coefficient (really the 5th term), it would be\r\n" );
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document.write( "If you needed the 5th term's coefficient (really the 6th term), it would be\r\n" );
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document.write( "etc., etc.\r\n" );
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document.write( "So to get the numerator of any term's coefficient, you start with\r\n" );
document.write( "the outer exponent, and multiply it by 1 less, then 1 less, etc.\r\n" );
document.write( "until you have as many factors as the number of term (starting\r\n" );
document.write( "counting from zero, not 1). Then the denominator is just that\r\n" );
document.write( "number factorial.  There are always as many factors on top\r\n" );
document.write( "as the number of term (starting counting form 0, not 1). And\r\n" );
document.write( "of course the denominator has that same number of factors, too.\r\n" );
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document.write( "Edwin

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