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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 \dots

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