## anonymous one year ago Help!! 1^2 + (1^2+2^2) + (1^2+2^2+3^2) + (1^2+2^2+3^2+4^2) + ......

1. anonymous

In the given progression find |dw:1438007233401:dw|

2. anonymous

??

3. anonymous

got any idea?

4. mathmate

Do you know how to do: $$\sum_{k=1}^n k, \sum_{k=1}^n k^2, and \sum_{k=1}^n k^3$$ ?

5. anonymous

yeah

6. mathmate

Ok, then the given series can be rewritten as: $$\sum_{i=1}^n \sum_{j=1}^i j^2$$

7. mathmate

from which you can expand the second summation in terms of the sum of squares.

8. anonymous

|dw:1438009474652:dw|

9. anonymous

right?

10. mathmate

... and in terms of i. It will be a cubic polynomial in terms of i. Then you can sum the first summation, to get the answer as a 4th degree polynomial.

11. anonymous

Right thanks

12. mathmate

13. anonymous

|dw:1438010017231:dw|

14. mathmate

Yep, that's what I got, and it's well factorized as well, good job! :)