Help me with this SAT Math Problem

Test Preparation SAT Preparation
1

<p>The sum of the first 1,000 positive integers is 500,500. What is the sum of the first 2,000 positive integers?</p>

2

<p>Sum of first 1000 positive integers= 1 + 2 + 3 + .. + 1000 = 500,500
Sum of 2nd 1000 positive integers = 1001 + 1002 + .... + 2000
= (1+1000) + (2+1000) + (3+1000) + .... + (1000 + 1000)
= 1 + 2 + 3 + .. + 1000
+1000 +1000 +1000 + ... + 1000
= 500,500 + (1000)(1000) =1,500,500</p>

<p>Sum of 1st 2000 positive integers = sum of 1st 1000 + sum of 2nd 1000
= 500,500 + 1,500,500
= 2,001,000</p>

<p>(Of course, you can always verify this with the formula for sum of an arithmetic series : S = (n/2)( first + last)
=(2000/2) (1 + 2000) = (1000)(2001) = 2,001,000 )</p>