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  • Given positive integers r>1, n>2 and the coeff. of (3r)th and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal. Then<div class='

Given positive integers r>1, n>2 and the coeff. of (3r)th and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal. Then

Option: 1

n = 2r


Option: 2

n = 2r + 1


Option: 3

n = 3r


Option: 4

None of these


Answers (1)

best_answer

We have, Tr + 1 = 2nCr x

Tr = 2nCr–1 xr–1

Replacing r by 3r, T3r = 2nC3r–1 x3r–1

Replacing r by r + 2, Tr+2 = 2nCr+1 xr+1

2nC3r–1 = 2nCr+1

3r – 1 = r + 1 or 2n = (3r – 1) + r + 1

2r = 2 or 2n = 4r

r = 1 or n = 2r

But r > 1      n = 2r

 

 

 

Posted by

Riya

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