Question

What is the sum of the multiples of 3 between 3 and 999, inclusive?

Answer 1

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Answer 2

Brendas wants a detailed solution!

Answer 3

Actually she only wants answers not how to solve this..

Answer 4

How many numbers are we talking about.

From 1 to 1000 is 1000. Leaving out 1, 2, 3 and 1000, we have 996. Don't worry, I'll put the 3 back in a minute.

Every third intgeer from 4 to 999 is a mulitple of 3. Divdiing 996 by 3 gievs 332.

Putting the 3 back menas 333 multpiles of 3.

Looking at the sum of the fisrt few, we have

3 + 6 + 9 + 12 + ...

Which is 3 tiems the sum of 1 + 2 + 3 + 4 + ..

Now for that hadny-dadny sum of the fisrt n integers: \[(1/2)(n)(n + 1). \]

We're summing from 1 to 333, so the sum is\[ (1/2)(333)(334) = 55611 \]

now multiply that by 3.

166833 is the sum of all the multiples of 3 between 3 and 999, inclusive.