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What is the average of all integers between - 7 and 9 inclusive?
It is 1.
Consider the numbers from 1-500 inclusive what is the difference between the sum of all of the even numbers and the sum of all the odd numbers?
501
What is the sum of the sequence 33 34 35 36 ... 112?
Adding all integers from 33 to 112 inclusive gives you 5800.
Add all integers 1 to 500?
There's a trick to this one. Let 1 + 2 + ... + 500 be the sum of all integers 1 to 500, called X Now, imagine we want to add the sum the integers from 1 to 500 and to the sum of the integers from 1 to 500. This would give us 2*X we can write it as 1 + 2 + ... + 500 + 1 + 2 + ... + 500 But that's not particularly useful. What if we look at it as: 1 + 2 + ... + 499 + 500 + 500 + 499 + ... + 2 + 1 adding the numbers that are directly on top of each other, we get 500 + 1 = 501, 499 + 2 = 501... 1 + 500 = 501 Thus every term is 501, and we have 500 terms. So, we have 501*500 = 2X Thus X, the sum from 1 to 500, is (500*501)/2 = 125,250
What is the even integers less than or equal to 11?
10, 8, 6, 4, 2, 0 and all the negative even integers.
