Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Prove that, 
n C 1 − 
n C 2 + 
n C 3 − 
n C 4 +..... + 
. n C n = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(1+x) n = C 0 + C 1 x + C 2 x 2 + ...........+ C n x n
⇒ n(1 + x) n–1 = C 1 + 2.C 2 x + 3.C 3 x 2 + .......+ n.C n x n–1
Now multiply by x & integrate from 0 to x
n(1 + x) n–1 . x = C 1 x + 2C 2 x 2 +...........+ nC n x n
⇒ 
+.........+ 
= x(1+x) n – 
Putting x = –1
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