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Often simple ideas lead to important mathematical results. A teacher in Germany during the early 1800's gave his class a problem to keep them busy. The problem sounded difficult to him and yet a 10 year old student gave him the correct answer within a very short time (about 2 minutes). When the teacher asked how he did it, the student could produce no work saying instead that he worked it out in his head.
Here is the problem, let's see how well you can do with it.
Add all the numbers from 1 to 100.
In other words 1+2+3+4+5+ .... +95+96+97+98+99+100= ????
Look closely at the numbers. There are patterns you can use that will help you add them. Your score on this assignement is based on how clever your solution is.
If you figure out the problem you should also be able to add all the numbers from 1 to 1000 in less that a minute - Can you?
Make sure your answer includes a
written outline of how you solved the problem.