How to find the values of these kind of summations: <mstyle mathsize="1.2em"> <munderover>

Joel French 2022-07-01 Answered
How to find the values of these kind of summations:
i = 0 6 ( 6 i ) j = 1 6 ( 7 j ) k = 2 7 ( 8 k ) = 3 8 ( 9 )
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Answers (1)

Jaruckigh
Answered 2022-07-02 Author has 11 answers
Use that
t = a b ( c t ) = ( t = a b c ) ( t = a b t ) = ( t = a b c ) ( s = 0 b a ( s + a ) ) = ( t = a b c ) ( s = 0 b a s ) ( s = 0 b a a ) = ( b a + 1 ) c ( b a + 1 ) a ( s = 0 b a s ) = ( b a + 1 ) ( c a ) ( s = 0 b a s ) = ( b a + 1 ) ( c a ) ( b a ) ( b a + 1 ) 2 = ( b a + 1 ) ( c a b 2 + a 2 ) = ( b a + 1 ) ( c b 2 a 2 )
for each term. For example,
i = 0 6 ( 6 i ) = 6 + 5 + 4 + 3 + 2 + 1 = 21 = 7 3 = ( 6 0 + 1 ) ( 6 6 2 0 2 )

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