document.write( "Question 666531: Prove that nC r + nCr-1 = n+1Cr \n" ); document.write( "

Algebra.Com's Answer #414530 by sachi(548) $\"\"$ $\"About$

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nCr+nCr-1=n+1Cr
\n" ); document.write( "or LHS=n!/[r!(n-r)!]+n!/[(r-1)!(n-r+1)!]
\n" ); document.write( "=n!/[r(r-1)!(n-r)!]+ n!/[(r-1)!(n-r+1)(n-r)!]
\n" ); document.write( "=n!/[(r-1)!(n-r)!]{[1/r]+[1/(n-r+1)]}
\n" ); document.write( "=n!/[(r-1)!(n-r)!]{(n+1)/r(n-r+1)}
\n" ); document.write( "=(n+1)n!/[r(r-1)!(n-r+1)(n-r)!]
\n" ); document.write( "=(n+1)!/[r!(n-r+1)!]
\n" ); document.write( "=n+1Cr
\n" ); document.write( "ans \n" ); document.write( "

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