SOLUTION: What is the value of the sum 1 + 2 3 + 4 5 + 6 7
+10,000?
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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?
------------
Each successive pair sums to "1"
There are 5000 pairs
The total sum is 5000
-----------------------------
OR
Add the positive terms: 2+4+6+...+10000
S(5000) = (5000/2)(2+10000) = 5000*5001
--------------------------------
Add the negative terms: 1+3+5+...+9999
S(5000) = (5000/2)(1+9999) = 2500*10000
---------------------------------
Subtract the sum of the negatives from the sum of the positives to get:
5000*5001 - 2500*10000 = 5000
===============================================
Cheers,
Stan H.
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