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Question 203306: What is the value of the sum –1 + 2 – 3 + 4 – 5 + 6 – 7 …+10,000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the value of the sum –1 + 2 – 3 + 4 – 5 + 6 – 7 …+10,000?
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Each successive pair sums to "1"
There are 5000 pairs
The total sum is 5000
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OR
Add the positive terms: 2+4+6+...+10000
S(5000) = (5000/2)(2+10000) = 5000*5001
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Add the negative terms: 1+3+5+...+9999
S(5000) = (5000/2)(1+9999) = 2500*10000
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Subtract the sum of the negatives from the sum of the positives to get:
5000*5001 - 2500*10000 = 5000
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Cheers,
Stan H.
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