ANSWERS: 2
  • Sum of integers from 1 to n is (n)(n+1)/2. In this case, n = 99, so 99*100/2 = 99*50, or 4950.
  • [The answer Foocubus submitted is way better than this one because he uses the simple formula (n)(n+1)/2 to find the sum of 1 to n. My answer is just using common sense in case you forget the equation.] Just add the ends together, eg 1+99=100 and 2+98=100 etc. rather than 1+2+3... and count the number of 100's you end up with. And if you're taking pairs at a time, how many pairs are there? 99/2 = 49.5 , so you got 49 pairs of numbers each adding to 100 (thus making 49 100's, or 4900) plus one half of a pair, meaning one whole number left over without a partner. What is the leftover number? Use a simpler problem. If the equation was 1+2+3+4+5, then you'd take 1+5, 2+4, and 3 is left over. So you take half the top number and add .5 to find the number in the middle. So with 99 we take 99/2 again to get 49.5, so the middle number is 50. So you got 49 pairs of 100, making 4900, plus the leftover 50. So 4950 is your answer.

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