dstebbins Posted April 29, 2012 Share Posted April 29, 2012 Is there an easier way to find the sum of all whole numbers between x and y (including x and y themselves) than to just sit there and painstakingly add every one up individually? Like, for example, I know that an easier way to find the cumulative product of all whole numbers between 1 and x all multiplied together is to simply punch in the equation "x!" into a calculator, so you don't have to painstakingly multiply 1*2*3*4*5...*x. Is there a similar "shortcut" for addition? Link to comment Share on other sites More sharing options...

Bignose Posted April 29, 2012 Share Posted April 29, 2012 You are talking about an arithmetic series. Lots of properties of these series have been looked at. http://mathworld.wolfram.com/ArithmeticSeries.html is as good a start as any. Link to comment Share on other sites More sharing options...

Lê_ Posted May 18, 2012 Share Posted May 18, 2012 the sum of all integers between x and y included is equal to (y-x+1)*(x+y)/2. Here's why: (x+y)/2 is the means of integers between x and y, and there are y-x+1 terms. Link to comment Share on other sites More sharing options...

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