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

Maths Sequence and Series ( Progressions ) NTA Abhiyas Question 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 the value of x is equal to

2005

2004

2003

2001

Text Solution

Verified by Experts

The correct answer is:

2005

Let,

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

K =1 2 + 2 2 + 3 2 + .... + 2003 2

Adding both, we get,

S + K = (2004) [1 + 2 + 3 + .... + 2003]

(2004) [1 + 2 + 3 + .... + 2003] = (2003) (334) (x) +(2003) (4007) (334)

x = 2005 .

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