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

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

helder_edwinBest 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
 one year ago

acrossBest 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.
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
Can I provide the link or not here ??
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
@across can I provide here the link or I have to derive here full??
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i think this was done in physics section ...
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
This is nothing but sum of squares of first n natural numbers..
 one year ago

helder_edwinBest 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
 one year ago

experimentXBest 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 ...
 one year ago

acrossBest ResponseYou've already chosen the best response.0
Links are more appreciated than derivations here. ^^
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
http://www.ilovemaths.com/3sequence.asp May be it will help you.
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
http://www.9math.com/book/sumsquaresfirstnnaturalnumbers Or you can check this also..
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm#general_term
 one year ago

experimentXBest 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 ....
 one year ago

asnaseerBest 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
 one year ago

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