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across
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Let's go over the derivation of\[\sum_{i=1}^{n}i^2=\frac{n(n+1)(2n+1)}{6}\]
 2 years ago
 2 years ago
across Group Title
Let's go over the derivation of\[\sum_{i=1}^{n}i^2=\frac{n(n+1)(2n+1)}{6}\]
 2 years ago
 2 years ago

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across Group TitleBest ResponseYou've already chosen the best response.0
This could follow from Gauss' assertion that\[\sum_{i=1}^{n}i=\frac{n(n+1)}{2}\]
 2 years ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.0
i don't remember the details. but i'm pretty sure u can find this in Spivaks' Calculus
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
It's easy to prove this by induction with your eyes closed, but I'm wondering how it's derived.
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Can I provide the link or not here ??
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
@across can I provide here the link or I have to derive here full??
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i think this was done in physics section ...
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
This is nothing but sum of squares of first n natural numbers..
 2 years ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.0
yes i know the proof is easy. i suggested spivak's book because i remember seeing the derivation there
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i would prefer geometrical visualization instead ... i remember seeing one is mit ocw single variable calculus. the volume of pyramid ...
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
Links are more appreciated than derivations here. ^^
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
http://www.ilovemaths.com/3sequence.asp May be it will help you.
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
http://www.9math.com/book/sumsquaresfirstnnaturalnumbers Or you can check this also..
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm#general_term
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
difference of power is very power technique ... it can be used to find the sums of n^3 and n^4 also ....
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
There is a very beautiful visual proof of this that @Ishaan94 came across when he asked this question: http://openstudy.com/updates/5002f7dae4b0848ddd66eea4
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
very interesting proof indeed !! \[ 3 \left ( \sum_{n=1}^\infty n^2 \right ) = (1 + 2 +3 +... + n)(2n+1)\]
 2 years ago
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