Hi guys,
I am having a little trouble understanding a multi sigma notation. I have a double sigma notation, the first sigma is directly followed by a second sigma with no arithmetic operator between them. i am given:
S(n) = (First Sigma) (Second Sigma) i
[the "i" is the formula after the second sigma. indexes : first sigma==>lower index :: k=1, upper index=n
second sigma==> lower index:: i=1, upper index=k]
So this seems to be =\sum^n_{k=1}\sum^k_{i=1}i)
+(1+2+3)+\ldots +(1+2+\ldots+ n))
. Now, use that for any }{2})
and (2n+1)}{6})
(you can easily prove both formulae by induction), and =\sum^n_{k=1}\frac{k(k+1)}{2}=\frac{1}{2}\left (\sum^n_{k=1}k^2+\sum^n_{k=1}k\right))
, plus a little algebra to deduce the result they want. The double notation may be understood as follows: make the first index run, and for each value it takes make the second sum's index run. Tonio
i am asked to prove that
![S(n) =[ n(n + 1)(n + 2)]/6](http://latex.codecogs.com/png.latex?S(n) =[ n(n + 1)(n + 2)]/6)
(I don't know how to make the sigma signs appear in this forum.)
I am asking if someone can explain to me what the double sigma notation means.
My understanding is this:
I replace the second sigma with a formula, so that the formula preceded by the first sigma is used for the proof .
Is that right?
Need help.
Thanks.
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Originally Posted by kap 
