Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Sum of the series S= 1 2 – 2 2 + 3 2 – 4 2 +……–2002 2 + 2003 2 is :
Text Solution
Verified by ExpertsThe correct answer is:
A
We can write S as
S = (1 – 2)(1 + 2) + (3 – 4)(3 + 4)……
(2001 – 2002) (2001 + 2002) + 2003 2 ⇒ S = (–1)(1 + 2) + (–1)(3 + 4) …..(–1)
(2001 + 2002) + 2003
2 S = (–1)[1 + 2 + 3 + 4 + 5 +…..2002]+ 2003
2 = (−1) 
+ (2003)
2 = – (1001×2003) + (2003)
2 = (2003)(2003 – 1001)
= 2003 × (1002)
= 2007006
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