anonymous
  • anonymous
Help!! 1^2 + (1^2+2^2) + (1^2+2^2+3^2) + (1^2+2^2+3^2+4^2) + ......
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
In the given progression find |dw:1438007233401:dw|
anonymous
  • anonymous
??
anonymous
  • anonymous
got any idea?

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mathmate
  • mathmate
Do you know how to do: \(\sum_{k=1}^n k, \sum_{k=1}^n k^2, and \sum_{k=1}^n k^3 \) ?
anonymous
  • anonymous
yeah
mathmate
  • mathmate
Ok, then the given series can be rewritten as: \(\sum_{i=1}^n \sum_{j=1}^i j^2\)
mathmate
  • mathmate
from which you can expand the second summation in terms of the sum of squares.
anonymous
  • anonymous
|dw:1438009474652:dw|
anonymous
  • anonymous
right?
mathmate
  • 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.
anonymous
  • anonymous
Right thanks
mathmate
  • mathmate
If you want a check, post your answer! :)
anonymous
  • anonymous
|dw:1438010017231:dw|
mathmate
  • mathmate
Yep, that's what I got, and it's well factorized as well, good job! :)

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