Direct expression for sum of squares

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Homework Help Overview

The discussion revolves around the formula for the sum of squares, specifically the transition from the summation notation \(\sum_{i=1}^n i^2\) to the closed-form expression \(\frac{n(n + 1)(2n + 1)}{6}\). Participants are exploring the correctness and implications of this formula.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the notation used in the summation and whether the expression provided is correctly simplified. There is a suggestion to prove the formula by induction, indicating a focus on validation of the formula.

Discussion Status

The discussion is active with participants correcting each other's notation and clarifying the index used in the summation. There is acknowledgment of mistakes, and some participants are providing references to external sources for further information.

Contextual Notes

There is a noted confusion regarding the index of summation, which has led to some participants questioning the correctness of the initial expression. The context suggests that the discussion is framed within homework constraints, emphasizing the need for clarity in mathematical notation.

cscott
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How do you go from [tex]\sum_{n = 1}^n i^2[/tex] to [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]?
 
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Prove the formula by induction.
 
I think you forgot to include something, what you wrote should simplify to [itex]n i^2[/itex].

Edit: Unless I'm missing something :confused:
 
Oops, the index should be i, not n as you've written.
 
Thanks for the info.

My mistake with the index.
 

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