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Imagine all of the 100 numbers from 1 to 100 written horizontally towards the right. Then imagine another100 numbers written below the first row, but starting with 100 at the left and finishing with the number 1 on the right hand end. Now you can see what looks like 100 additions of two numbers. If you worked out those additions they would all total exactly 101, which means that altogether we have 100 pairs of numbers each totalling 101, and therefore the grand total of all 200 numbers is 101 x 100 = 10100; but 10100 is the total of two sets of numbers from 1 to 100; we want the total of one set of numbers; so we divide the 10100 by 2 which is 5050; the beauty of this method is that you don't need complicated calculations; all you need to be able to do is to multiply by 100 and to divide by 2; a very neat solution to the problem!

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