If 1 2 + 2 2 + 3 2 + ….. + 2003 2 = (2003) (4007) (334) and…

Maths Sequence and Series ( Progressions ) nth Term of Special Series, Sum to n Terms and Infinite Number of Terms Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If 1 2 + 2 2 + 3 2 + ….. + 2003 2 = (2003) (4007) (334) and (1) (2003) + (2) (2002) + (3) (2001) + …+ (2003) (1) = (2003) (334) (x) then x equals -

2005

2004

2003

2001

Text Solution

Verified by Experts

The correct answer is:

Let

S = (1) (2003) + (2) (2002) + (3) (2001) + …. + (2003) (1)

and

K = 1 2 + 2 2 + 3 2 + …. + 2003 2

Adding, we get

S + K = (2004) [1 + 2 + 3 +…. + 2003]

⇒ (2003) (334) (x) + (2003) (4007) (334)

= (2004) (1002) (2003)

⇒ x = 2005.

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