document.write( "Question 940228: Prove that the following relationship is true:\r
\n" ); document.write( "\n" ); document.write( "nCr + nC(r+1) ?=? (n+1)C(r+1)\r
\n" ); document.write( "\n" ); document.write( "Use the least common denominator method. \n" ); document.write( "
Algebra.Com's Answer #573028 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "nCr + nC(r+1) ?=? (n+1)C(r+1)\r\n" );
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document.write( "(1)   nCr = \"n%21%2F%28r%21%28n-r%29%21%29\"\r\n" );
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document.write( "(2)   nC(r+1) = \"n%21%2F%28%28r%2B1%29%21%28n%5E%22%22-%28r%2B1%29%29%21%29\" = \"n%21%2F%28%28r%2B1%29%21%28n-r-1%29%21%29\"\r\n" );
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document.write( "(3)   (n+1)C(r+1) = \"%28n%2B1%29%21%2F%28%28r%2B1%29%21%28%28n%2B1%29%5E%22%22-%28r%2B1%29%29%21%29\" = \"%28n%2B1%29%21%2F%28%28r%2B1%29%21%28n%2B1-r-1%29%21%29\" = \"%28n%2B1%29%21%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "We want to prove that expression(1) + expression(2) = expression(3)\r\n" );
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document.write( "nCr + nC(r+1) = \r\n" );
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document.write( "\"n%21%2F%28r%21%28n-r%29%21%29\"\"%22%22%2B%22%22\"\"n%21%2F%28%28r%2B1%29%21%28n-r-1%29%21%29\"\r\n" );
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document.write( "Substitute (n-r)(n-r-1)! for (n-r)! and (r+1)r! for (r+1)!  \r\n" );
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document.write( "\"n%21%2F%28r%21%28n-r%29%28n-r-1%29%21%29\"\"%22%22%2B%22%22\"\"n%21%2F%28%28r%2B1%29r%21%28n-r-1%29%21%29\" \r\n" );
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document.write( "LCD = (r+1)r!(n-r)(n-r-1)!\r\n" );
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document.write( "\"%28n%21%28red%28r%2B1%29%29%29%2F%28+%28red%28r%2B1%29%29r%21%28n-r%29%28n-r-1%29%21%29\"\"%22%22%2B%22%22\"\"n%21%28red%28n-r%29%29%2F%28%28r%2B1%29r%21%28red%28n-r%29%29%28n-r-1%29%21%29\" \r\n" );
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document.write( "Replace (r+1)r! by (r+1)! and replace (n-r)(n-r-1) by (n-r)!\r\n" );
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document.write( "\"%28n%21%28r%2B1%29%29%2F%28+%28r%2B1%29%21%28n-r%29%21%29\"\"%22%22%2B%22%22\"\"n%21%28n-r%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\" \r\n" );
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document.write( "\"%28n%21%28r%2B1%29%2Bn%21%28n-r%29%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\" \r\n" );
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document.write( "\"%28n%21r%2Bn%21%2Bn%21n-n%21r%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "\"%28cross%28n%21r%29%2Bn%21%2Bn%21n-cross%28n%21r%29%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "\"%28n%21%2Bn%21n%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "\"%28n%21%281%2Bn%29%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "\"%28%28n%2B1%29n%21%29%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "\"%28n%2B1%29%21%2F%28%28r%2B1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "(n+1)C(r+1)\r\n" );
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document.write( "Edwin
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