arithmetic series

Printable View

April 22nd 2008, 07:11 PM
Cheeta921

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…
This is where I draw a blank. I have No idea. Please help.
April 22nd 2008, 07:14 PM
Mathstud28

Quote:

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…
This is where I draw a blank. I have No idea. Please help.

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
April 22nd 2008, 07:16 PM
Krizalid

Quote:

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…
This is where I draw a blank. I have No idea. Please help.

You're expected to know that $\sum_{k\,=\,1}^n k=\frac{n(n+1)}2,$ this will do those stuff.
April 22nd 2008, 07:20 PM
Cheeta921

Thank you, Krizalid, But i don't know what you mean by that formula. Could you please explain?
April 22nd 2008, 07:23 PM
Krizalid

Quote:

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.
April 22nd 2008, 07:24 PM
Mathstud28

Quote:

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... $1+2+3+4+5+6+...+(n-1)+n=\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$
April 22nd 2008, 07:26 PM
Cheeta921

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.(Headbang)