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Question 666237: what is the sum of the first 1000 consecutive whole numbers?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! In general, the sum of the first n numbers is n(n+1)/2. Then 1000(1000+1)/2 = 500*1001 = 500500.
If you don't believe the result, here's a nice proof:
Let S be the sum of the first n numbers.
S = 1+2+3+...+n
Also, notice that we can use the commutative property to write S in a different way.
S = n+n-1+n-2+n-3+...+1
If we add these two equations we get
2S = n+1 + n+1 + n+1 +...+ n+1
How many times do we get n+1? n times.
2S = n*(n+1)
S = n*(n+1)/2 :)
So, this form will work for any sum 1 to #whatever.
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