across
  • across
Let's go over the derivation of\[\sum_{i=1}^{n}i^2=\frac{n(n+1)(2n+1)}{6}\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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across
  • across
This could follow from Gauss' assertion that\[\sum_{i=1}^{n}i=\frac{n(n+1)}{2}\]
helder_edwin
  • helder_edwin
i don't remember the details. but i'm pretty sure u can find this in Spivaks' Calculus
across
  • across
It's easy to prove this by induction with your eyes closed, but I'm wondering how it's derived.

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anonymous
  • anonymous
Can I provide the link or not here ??
anonymous
  • anonymous
@across can I provide here the link or I have to derive here full??
experimentX
  • experimentX
i think this was done in physics section ...
anonymous
  • anonymous
This is nothing but sum of squares of first n natural numbers..
helder_edwin
  • helder_edwin
yes i know the proof is easy. i suggested spivak's book because i remember seeing the derivation there
experimentX
  • experimentX
i would prefer geometrical visualization instead ... i remember seeing one is mit ocw single variable calculus. the volume of pyramid ...
across
  • across
Links are more appreciated than derivations here. ^^
anonymous
  • anonymous
http://www.ilovemaths.com/3sequence.asp May be it will help you.
anonymous
  • anonymous
http://www.9math.com/book/sum-squares-first-n-natural-numbers Or you can check this also..
experimentX
  • experimentX
http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm#general_term
experimentX
  • experimentX
difference of power is very power technique ... it can be used to find the sums of n^3 and n^4 also ....
asnaseer
  • asnaseer
There is a very beautiful visual proof of this that @Ishaan94 came across when he asked this question: http://openstudy.com/updates/5002f7dae4b0848ddd66eea4
experimentX
  • experimentX
very interesting proof indeed !! \[ 3 \left ( \sum_{n=1}^\infty n^2 \right ) = (1 + 2 +3 +... + n)(2n+1)\]

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