document.write( "Question 1185059: find the sixteenth term of (2-1/x)^18 \n" ); document.write( "
Algebra.Com's Answer #815812 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "find the sixteenth term of (2-1/x)^18.
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\n" ); document.write( "\n" ); document.write( "            Each such problem  HAS  a  TRAP.          A L W A Y S. \r
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\n" ); document.write( "\n" ); document.write( "            In the given problem,  the trap is that the  16-th term  IS  NOT  THE  TERM  with   \"1%2Fx%5E16\".\r
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\n" ); document.write( "\n" ); document.write( "            Read my solution below attewntively and consider it as a standard  MANTRA  to solve such problems.\r
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\n" ); document.write( "\n" ); document.write( "            Following this mantra will allow you to avoid similar traps in the future.\r
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document.write( "The binomial expansion is this formula\r\n" );
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document.write( "    \"%28a%2Bb%29%5En\" = \"a%5En\" + \"C%5Bn%5D%5E1%2Aa%5E%28n-1%29%2Ab\" + \"C%5Bn%5D%5E2%2Aa%5E%28n-2%29%2Ab%5E2\" + \"C%5Bn%5D%5E3%2Aa%5E%28n-3%29%2Ab%5E3\" + . . . + \"C%5Bn%5D%5E%28n-1%29%2Aa%5E1%2Ab%5E%28n-1%29\" + \"b%5En\"\r\n" );
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document.write( "In our case,  n = 18,  a = 2,  b = -\"1%2Fx\",  therefore, the common term of the binomial expansion in our case is  \r\n" );
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document.write( "    \"C%5B18%5D%5Ek%2A2%5E%2818-k%29%2A%28-1%29%5Ek%2A%281%2Fx%29%5Ek\", k = 0, 1, 2, 3, 4, 5, . . . , 17, 18.\r\n" );
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document.write( "Notice that k= 0 for the 1-st term;  k= 1 for the 2-nd term, and so on.  Then the 16-th term is at k = 15 \r\n" );
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document.write( "    \"C%5B18%5D%5E15%2A2%5E%2818-15%29%2A%28-1%29%5E15%2A%281%2Fx%29%5E15\" = - \"%28%2818%2A17%2A16%29%2F%281%2A2%2A3%29%29%2A2%5E3%2A%281%2Fx%29%5E15\" = - \"816%2A2%5E3%2A%281%2Fx%29%5E15\" = - \"6528%2A%281%2Fx%5E15%29\".\r\n" );
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document.write( "ANSWER.  The 16-th term is  - \"6528%2A%281%2Fx%5E15%29\". \r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar solved problems and to learn the subject wider and deeper,  then look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on binomial coefficients \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic
\n" ); document.write( "\"Binomial expansion, binomial coefficients, Pascal's triangle\".\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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