For any positive integer n, the sum of the first n positive integers equals ~$\frac{n\left ( n+1 \right )}{2}$~. What is the sum of all the even integers between 99 and 301?
sum of all even integer 1 to 301 = 2 * (1+2+...+150) = (2*150*151)/2 = 150*151
sum of all even integer 1 to 99 = 2 * (1+2+....+49) = (2*49*50)/2 = 49*50
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sum of all even integer 1 to 301 = 2 * (1+2+...+150) = (2*150*151)/2 = 150*151
sum of all even integer 1 to 99 = 2 * (1+2+....+49) = (2*49*50)/2 = 49*50
required sum = 150*151 - 49*50 = 50*(453 - 49) =
404 * 50 = 20200
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