document.write( "Question 1044456: Prove that nCr/nCr+nCr+1 = r+1/n+1
\n" ); document.write( "Please help me with this as soon as possible \n" ); document.write( "

Algebra.Com's Answer #659784 by Boreal(15235) $\"\"$ $\"About$

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nCr=n!/r!(n-r)!
\n" ); document.write( "nC(r+1)=n!/(r+1)!(n-r-1)!, the sign in this is different from the prior problem. Use numbers to show why, for example 7C3.
\n" ); document.write( "The denominator is
\n" ); document.write( "n!/r!(n-r)!+n!/(r+1)!(n-r-1)!
\n" ); document.write( "This has a common denominator of (r+1)!(n-r)!
\n" ); document.write( "Using that common denominator, the numerator is n!(r+1)+n!(n-r), because r! divides into (r+1)! r+1 times and n-r-1 divides into (n-r) n-r times.
\n" ); document.write( "The numerator of the whole thing is
\n" ); document.write( "n!/r!(n-r)!
\n" ); document.write( "The denominator is n!(r+1)+n!(n-r) all divided by (r+1)!(n-r)!
\n" ); document.write( "Every n! cancels because there is one in each term.
\n" ); document.write( "you now have
\n" ); document.write( "1/r!(n-r)! divided by {(r+1)+(n-r)]/(r+1)!(n-r)!}
\n" ); document.write( "the (n-r)! cancel and the fraction is (n+1)/(r+1)!
\n" ); document.write( "You now have
\n" ); document.write( "1/r! divided by (n+1)/(r+1)!
\n" ); document.write( "Invert and this is (r+1)!/r!(n+1)
\n" ); document.write( "but (r+1)! is (r+1)*r!, and the r! cancel, so you have
\n" ); document.write( "(r+1)/(n+1) \n" ); document.write( "

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