The expansion of (1+x)n has 3 consecutive terms with coefficients in the ratio 1:2:3 and can be written in the form Ck n:Ck+1 n:Ck+2 n . The sum of all possible values of (n+k) is
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answer is 18.
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Detailed Solution
Cn,kCn,k+1=12n!n−k!k!×k+1!n−k−1!n!=12k+1n−k=122k+2=n−k3k+2=nCn,k+1Cn,k+2=23n!n−k−1!k+1!×k+2!n−k−2!n!=23k+2n−k−1=233k+6=2n−2k−25k+8=2nSolving the above two equations, we get n= 14, k=4