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CGP EDU Academic Team
Published on: August 14, 2026
If ( 2n C 1 )²+ 2. ( 2n C 2 )² + 3. ( 2n C 3 )² +... + 2n. ( 2n C 2n )² = 18 . 4n–1 C 2n–1 , then n is :
Text Solution
Verified by ExpertsThe correct answer is:
9
(9)
(1+x) 2n = 2n C 0 + 2n C 1 x + ............+ 2n C 2n x 2n
differentiating it
2n(1+x) 2n–1 = 2n C 1 + 2. 2n C 2 x + ............+ 2n 2n C 2n x 2n–1
Again (x+1) 2n = 2n C 0 x 2n + 2n C 1 x 2n–1 + 2n C 2 x 2n–2 + ............+ 2n C 2n
Required expression = coefficient of x 2n–1 in 2n (1+x) 4n–1
= 2n. 4n–1 C 2n–1
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