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The coefficient of 5th, 6th and 7th terms in the expansion of (1+X)^n are in AP. Find n

The coefficient of 5th, 6th and 7th terms in the expansion of (1+X)^n are in AP. Find n

Grade:12th pass

1 Answers

sonika p
129 Points
6 years ago
nC5 + nC7 = 2*nC6
(n!/5!(n-5)!) + (n!/7!(n-7)!) = 2* (n!/6!(n-6)!)
(1/(n-6)(n-5)) + (1/7*6) = 2* (1/6*(n-6))
solving the equation, 
42 + (n-5)(n-6) = 14(n-5)
n^2 -25n + 142= 0
n=16.2749, n = 8.725
 

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