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The total T of adding numbers from 1 to n is (n x (n+1))/2; consider if n=10:

adding 1+ 2+ 3+...+ 8+ 9+ 10= T and

adding 10+ 9+ 8+...+ 3+ 2+ 1= T (the same answer)

Now add the the two lines together--->

11+11+11+..+11+11+11= 2T, so there are 10 11s

10 x 11 =2T, divide both sides of the equal sign by 2

(10 x 11)/2 =T

So, where n=10, T=55

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Q: What is the total of all numbers added from 1 to 100?
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