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gauss approach using n/2

Algebra
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1+3+5+7+...999

Nov 26th, 2014

Notice that 1 + 999 = 1000, 3 + 997 = 1000, 5 + 995 = 1000, etc. 

You have to figure out how many pairs there are in your sum.  We can figure this out if we take 1-99 and then extrapolate.  Since there are 100 number is 1-100, there would be 50 number in 1-100 odd; we're pairing 2 numbers of the 50, so we would have 25 pairs of numbers in 1-100.  If we multiply that by 10 (because we're looking at 1-1000, not 1-100), we would have 2500 pairs of numbers that add up to 1000.

Therefore, we take 2500*1000 = 2,500,000


Hope this helps!

Nov 26th, 2014

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