Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If C 0 , C 1 , C 2 ..... C n are the coefficient in the expansion of (1+ x) n then prove that C 2 0 + C 1 2 + C 2 2 + ........ C n 2 = 2n C n
Text Solution
Verified by ExpertsThe correct answer is:
1
Sol. (1 +x) n = C 0 + C 1 + C 2 x 2 + C 3 x 3 + ........... + C n x n
(x + 1) n = C 0 x n +C 1 x n– 1 + C 2 x n– 2 + ... + C n multiplying both (C 0 + C 1 x + C 2 x 2 + ... + C n x n ) (C 0 x n + C 1 x n – 1 + C 2 x n – 2 ..... + C n ) = (1+ x) 2n equating coefficient of x
n C 0 2 + C 1 2 + C 2 2 + C 3 2 + ......... C n 2 = 2n C n
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems