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Weekly Problem 20 - 2013

Stage: 3 Challenge Level: Challenge Level:1

The diagram shows that $1 + 3 + 5 + 7 + 5 + 3 + 1 = 3^2 + 4^2$.

What is $1 + 3 + 5 + \dots + 1999 + 2001 + 1999 + \dots + 5 + 3 + 1$?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.

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