If the middle term of (1+ x) 2n (x > 0, n ∈ N) is the greatest term of the expansion. Then the interval in which n lies, is-
Text Solution
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Middle term = 2n C n .x n = t n+1
t n+1 is also greatest – therefore
t n+1 > t n …(1)
t n+1 > t n+2 …(2)
From (1)
⇒ 2n C n . x n > 2n C n–1 . x n–1 ⇒ 
. x > 
⇒ (n + 1) x > n ⇒ x > 
… (i)
From (2)
⇒ 2n C n . x n > 2n C n+1 . x n+1 ⇒ 
> 
x ⇒ x < 
… (ii)
So, from (i) and (ii), x ∈ 
Now, we know that the greatest term can also be equal to one of the adjacent terms. Hence the equality can also holds with equation (1) or equation (2)
∴ x ∈ 
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