# Math Help - arithmetic series

1. ## arithmetic series

Task: explain step-by-step how to find the sum of the number 1 to 2000 that are not divisible by 3 or 7. Be sure your plan includes steps to check your work.

Because you would already know how, I’ll give you the quick version of what I did. (not explaining exactly what each value is)
The only formula that I used was Sn= [n(a1+an)]/2

Step one. Find sum of numbers 1 to 2000 using formula. (Equals 2001000)
Step two, find sum of numbers 1-2000 that are divisible by 3 (Equals 666333)
Step three find sum of numbers 1-2000 that are divisible by 7 (Equals 285,285)
Step four Subtract answers 2 and 3 from 1.
Step five, find sum of numbers 1-2000 that are divisible by 21 and add it back so that you aren’t subtracting the same numbers twice.
To check…

2. Originally Posted by Cheeta921
Task: explain step-by-step how to find the sum of the number 1 to 2000 that are not divisible by 3 or 7. Be sure your plan includes steps to check your work.

Because you would already know how, I’ll give you the quick version of what I did. (not explaining exactly what each value is)
The only formula that I used was Sn= [n(a1+an)]/2

Step one. Find sum of numbers 1 to 2000 using formula. (Equals 2001000)
Step two, find sum of numbers 1-2000 that are divisible by 3 (Equals 666333)
Step three find sum of numbers 1-2000 that are divisible by 7 (Equals 285,285)
Step four Subtract answers 2 and 3 from 1.
Step five, find sum of numbers 1-2000 that are divisible by 21 and add it back so that you aren’t subtracting the same numbers twice.
To check…
add to it the numbers divisible by 4,5,6,7,8,9 this will provide the sum of all numbers if you did it correctly

3. Originally Posted by Cheeta921
Step one. Find sum of numbers 1 to 2000 using formula. (Equals 2001000)
Step two, find sum of numbers 1-2000 that are divisible by 3 (Equals 666333)
Step three find sum of numbers 1-2000 that are divisible by 7 (Equals 285,285)
Step four Subtract answers 2 and 3 from 1.
Step five, find sum of numbers 1-2000 that are divisible by 21 and add it back so that you aren’t subtracting the same numbers twice.
To check…
You're expected to know that $\sum_{k\,=\,1}^n k=\frac{n(n+1)}2,$ this will do those stuff.

4. Thank you, Krizalid, But i don't know what you mean by that formula. Could you please explain?

5. Originally Posted by Cheeta921
Step one. Find sum of numbers 1 to 2000 using formula. (Equals 2001000)
Suppose you want to find $1+2+3+\cdots+n,$ eventually for $n=2000$ we want to find $1+2+3+\cdots+2000.$ Do you understand what $\sum$ means? The formula I gave you solves those problems.

6. Originally Posted by Cheeta921
Thank you, Krizalid, But i don't know what you mean by that formula. Could you please explain?
It is the same formula you have in your passage... $1+2+3+4+5+6+...+(n-1)+n=\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$

7. Right, My book uses i instead of K... I used the other formula since it means the same thing, could i use this one as my check? Thank you for being patient with me.