doubts

The interval in which x(>0) must lie so that the greatest term in the expansion of (1+x)²ⁿ has the greatest coefficient is

(a)(n-1/n,n/n-1)
(b)(n/n+1,n+1/n)
(c)(n/n+2,n+2/n)
(d)None of these.

4 Answers

ans is (b)( n/{n+1} , {n+1}/n )

yes it is b.....how did u get it plz explain stepwise

u can take 2 approach ... long cut .. short cut

shortcut is take n = 1
1 + 2x + x²

2x is the term having greatest coefficient

2x > 1 ...... x >1/2
2x > x² ...... x < 2
1/2 < x < 2

only b satisfies// shortcut because u can do this mentally

longcut
mid term has largest coefficient
²ⁿC_n xⁿ > ²ⁿC_n+1 xⁿ⁺¹
(n+1)/n>x

similarly
n/n+1<x

first method is amazing ......thanx:)

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