document.write( "Question 1091827: Please help...
\n" ); document.write( "Find the coefficient of the given term in the binomial expansion
\n" ); document.write( "x^11y^3 term, (x+y)^14
\n" ); document.write( "Thank you.
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Please help...
\n" ); document.write( "Find the coefficient of the given term in the binomial expansion
\n" ); document.write( "x^11y^3 term, (x+y)^14
\n" ); document.write( "Thank you.
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First of all, it’ll have to be determined what TERM number produces \"x%5E11\".\r
\n" ); document.write( "\n" ); document.write( "Since the exponent on the binomial is 14, it follows that there will be 15 (FIFTEEN) terms, and the term number containing \"x%5E11\" will be the 15th – 11th term, or the 4th term.\r
\n" ); document.write( "\n" ); document.write( "To find a specific term in a BINOMIAL EXPANSION, we use the following formula:
\n" ); document.write( "\"%28a+%2B+b%29%5En+=+%22%22%5Bn%5DC%5Br+-+1%5D%28a%29%5E%28n-%28r-1%29%29%28b%29%5E%28r-1%29\", where r = term number
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\n" ); document.write( "\n" ); document.write( "As seen above, the 4th term of the sequence will have the following coefficient on x: \"%22%22+%5B14%5DC%5B4+-+1%5D\". This results in:
\n" ); document.write( "You could also check PASCAL’S triangle and look for the coefficient for the 4th term of a BINOMIAL EXPANSION with a binomial that’s being raised to the 14th power.
\n" ); document.write( "This is 364. \n" ); document.write( "
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