Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Prove that if n is a positive integer, 1– 
+ 
– 
+…….= 0
Text Solution
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Sol. Let S = 1 – 
+ 
+ 
– 
+ …..
= C 0 – C 1 
+ C 2 
– C 3 
+……
= C 0 – C 1 
+ C 2 
– C 3 
+……+
… (1)
Now (1 – y) n = C 0 – C 1 y + C 2 y 2 – C 3 y 3 +……..… (2)
On diff. we get – n (1 – y) n–1 = –C 1 + 2C 2 y –3C 3 y 2 +…..… (3)
Putting y = 
in equations (1) and (2) we get
= 
= C 0 – C 1 
+ C 2
+ …… … (4)
and – n 
= –C 1 + 
+…..
⇒ – n 
= –C 1 + 
– 
+ ……… (5)
From (1), (4) and (5), we get
S = 
+ 
= 
– 
= 0
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