S(1) = 1 = 12
S(2) = 1 + 3 = 4 = 22
S(3) = 4 + 5 = 9 = 32
S(4) = 9 + 7 = 16 = 42
etc
So S(2000) = 20002 = 4,000,000
I owe the insight to this answer to another contributor who, because of Wiki rules, cannot be named. How about *cienceguy22?
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Answer is 4000000: The sum of the first N odd numbers is N^2. Look at 1,3,5 for example. There are 3 numbers and the sum is 9 which is 3^2. Add 7 and the sum is 16 which is 4^2. So the of the first 2000 consecutive odd numbers is 2000^2 Note 2000 is 2(10^3). When we square that it is 4x10^6=4000000
The sum of the first 1,000 odd numbers is 1,000,000.
The sum of the first 50 odd numbers is 2,500.
The sum of the first 153 odd numbers is 23,409.
The sum of the first 8,000 odd numbers 64,000,000.