where can I learn about multiple sigma notaions of dependent and independent variables something like this Σ_(1≤i) Σ_(<j) Σ_(<k≤1) (i+j+k)=λ find λ I want to know what to study


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Question Number 194610 by justenspi last updated on 11/Jul/23

$w h e r e c a n I l e a r n a b o u t m u l t i p l e s i g m a n o t a i o n s$ $o f d e p e n d e n t a n d i n d e p e n d e n t v a r i a b l e s$ $s o m e t h i n g l i k e t h i s$ $\sum_{1 ⩽ i} \sum_{< j} \sum_{< k ⩽ 1} (i + j + k) = λ$ $f i n d λ$ $I w a n t t o k n o w w h a t t o s t u d y$
	Answered by qaz last updated on 11/Jul/23

	$\sum_{1 ⩽ i < j < k ⩽ n} (i + j + k) = [1 ⩽ i < j < k ⩽ n] (i + j + k)$ $= [1 ⩽ k ⩽ n] [i + 1 ⩽ j ⩽ k - 1] [1 ⩽ i ⩽ j - 1] (i + j + k)$ $= [3 ⩽ k ⩽ n] [2 ⩽ j ⩽ k - 1] [1 ⩽ i ⩽ j - 1] (i + j + k)$ $= [3 ⩽ k ⩽ n] [2 ⩽ j ⩽ k - 1] (\frac{1}{2} j (j - 1) + (j - 1) (j + k))$ $= [3 ⩽ k ⩽ n] (k^{3} - 3 k^{2} + 2 k)$ $= \frac{1}{4} (n - 2) (n - 1) n (n + 1), (n \in N, n ⩾ 3)$
	Commented by justenspi last updated on 11/Jul/23

	$t h a n k s, s i r$ $w h e r e c a n I l e a r n t h a t$ $i n w h a t b o o k$
	Commented by qaz last updated on 11/Jul/23

	$H a v e y o u s t u d i e d d o u b l e o r t r i p l e i n t e g r a l s ?$ $T h i s i s s i m i l a r t o e x c h a n g e t h e o r d e r o f i n t e g r a l s,$ $n o s p e c i a l b o o k s a r e r e q u i r e d . . .$
	Commented by justenspi last updated on 11/Jul/23

	$a c t u a l y I a m a h i g h s c h o o l s t u u d e n t$
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