Try to figure out a function f(n) which takes the input n, where n∈N, and outputs the sum ∑i=ni=0kji till the nth value where k∈R & j∈N

klastiesym 2022-10-19 Answered
Try to figure out a function f ( n ) which takes the input n, where n N , and outputs the sum i = 0 i = n k j i till the n t h value where k R & j N . For example i = 0 i = n 3 2 i
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Answers (1)

Jimena Torres
Answered 2022-10-20 Author has 20 answers
Let a R .
S ( n ) = a k 0 + a k j + a k 2 j + a k 3 j + + a k j n
k j S ( n ) = a k j + a k 2 j + a k 3 j + a k 4 j + + a k j n + j
So,
S ( n ) k j S ( n ) = a k 0 a k j n + j
S ( n ) ( 1 k j ) = a k 0 a k j n + j
S ( n ) = a k 0 a k j n + j ( 1 k j )
S ( n ) = a ( 1 k j n + j ) ( 1 k j )
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