Posted by **jadacess** on Friday, February 8, 2008 at 11:51pm.

The sum of the swuares of the first n counting numbers:

1² + 2² + 3² + 4² + 5² + 6² + ... +n²

is given by the formula

S = n(n+1)(2n+1)

------------

6

Find the sum of the squares of all the counting numbers between 15 and 35.

- answer is 12445;

how do you do this question ? ><

- algebra -
**Reiny**, Saturday, February 9, 2008 at 8:24am
Use the formula to find the sum of the squares from 1 to 35,

then find the sum of the squares of the numbers from 1 to 14

Subtract the smaller from the larger to get the in-betweens.

I had 14910 - 1015 = 13895

did you mean ... 15 to 35 inclusive or exclusive?

Mine is the inclusive, for the exclusive

subtract up to 15 from up to 34, that will give you the answer they provided.

- algebra -
**tchrwill**, Saturday, February 9, 2008 at 1:04pm
The sum of the swuares of the first n counting numbers:

1² + 2² + 3² + 4² + 5² + 6² + ... +n²

is given by the formula

S = [n(n+1)(2n+1]/6

The sum of the squares of the first "n" counting numbers minus the squares of the first "m - 1) counting numbers (or the sum of the squares from "m" to "n")is given by the formula

S = [2(n^3 - m^3) + 3(n^2 - m^2) + (n - m)]/6.

The sum of the squares from n = 1 to n = 7 is S(1-7) = 7(8)(15)/6 = 140.

The sum of the squares from "m" = 4 to n = 7 is S(4-7) = [558 + 195 + 3]/6 = 126.

The sum of the squares of all the counting numbers between 15 and 35.

Do you mean the sum of squares of the counting numbers "between" 15 and 35, or 16 through 35 or the counting numbers "from" 15 through 35, or 15 through 35. You decide and use the formula.

## Answer this Question

## Related Questions

- algebra - The sum of the first n counting numbers 1 + 2 + 3 + 4 + 5 ... + n is ...
- algebra - What is th remainder when the sum of the first 102 counting numbers is...
- Algebra - What is the remainder when the sum of the first 102 counting numbers ...
- math - The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the ...
- Math - 1.(A)(i)Show that 2+4+6+8+..+2n=n(n+1). (ii)Find the sum of the first 200...
- sum fun (math) - find a quick and easy method to compute the sum of the first ...
- Algebra - Sorry Iposted that previous question wrong. Here is the right question...
- PRE CAL SEQUENCES - Given the following finite sum 1/(1*2)+1/(2*3)+1/(3*4)+1/(4*...
- Math....Please help I have a deadline for tonight! - Use the geometric sequence ...
- math - "Find a quick and easy method to compute the sum of the first 100 ...

More Related Questions