Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If (1+x) n = C 0 + C 1 x + C 2 x² +.... + C n x n, then show that the sum of the products of the C i ’s taken two at a time, represented by 
is equal to 2 2n − 1 − 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(1+x) n = C 0 + C 1 x + .... + C n x n
S = 
C i C j = 
[(C 0 + C 1 + C 2 + ......+ C n ) 2 – (C 02 + C 12 + C 22 + ......+ C n2 )]
⇒ 2S = 2 2n – 2n C n ⇒ S = 2 2n–1 – 
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