the trick to this is to realize the pattern:
10000=0+10000
10000=1+9999
10000=2+9998
...
10000=4999+5001
so there are 5000 (10000s) and the unmatched 5000 in the middle
= 50,005,000
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To find the average of integers, add them all together then divide the total by the number of integers.
All of the integers between 20 and 30 are square roots.
No. The sum of all integers between 1 and 500 is 124,749.
If you write down all of the integers between the two numbers, your sum is equivalent to 5,659.
This is easiest to answer by summing all the numbers 1-10000 and subtracting the sum of the multiples of 7 (7, 14, 21, ..., 9996). The sum of a series is: S = (first + last) x number_of_terms / 2 For for 1-10000, the sum is: S1 = (1 + 10000) x 10000 / 2 = 10001 x 5000 = 50005000 For the multiples of 7 the sum is: S2 = (7 + 9996) x 1428 / 2 = 10003 x 714 = 7142142 So the sum of all integers not greater than 10000 that are not divisible by 7 is: S = S1 - S2 = 50005000 - 7142142 = 42,862,858