Maths Enrichment Euler?

Question

plz help me or at least give me some tips on this answer........

Find the sum of all positive integers not greater than 10000 that are divisible by either 3 or 11 but not both of them

Answer 1

we first find the sum of all numbers <= 10000 that are divisible by 3 and the sum of those divisible by 11 and add them. we then subtract from this twice the sum of all numbers <= 10000 divisible by 3*11 or 33.

Answer 2

First we count all positive number from 1 to 10000 that are divisible by3.

we get 3+6+9+12+...+9999. We know that the equation of 3,6,9,...,9999 is U(n)=3n

So we get n is 3333.

The sum of all that number is (3+9999)/2 *3333

let say the result is a

Second, we count all that are divisible by 11. we get 11+22+33+44+55+....+9999

U(n)=11n, we get n=909

So the sum is (11+9999)/2 *909, let say the result is b

if we add a and b, we will add all that is divisible by 3 or 11, and we also add all that are divisible by 3 and 11 two times. But, we don't want all of the numbers that are divisible by 33. So we can simply subtract those which are divisible by 33 2 times, let say it c.

You will get c=(33+9999)/2 *303.

So thethe sum of all positive integers not greater than 10000 that are divisible by either 3 or 11 but not both of them is a+b-2c