Respuesta :
The recurrence relation is given by
[tex]( ^{5} _{0} ) 5^{n} - ( ^{5} _{1}) 4^{n} + ( ^{5} _{2}) 3^{n} ( ^{5}_{3} ) 2^{n} + ......... + ( -1)^{6} (^{5} _{4}) 1^{k}[/tex]
What does a level of recurrence mean?
In this case, the prior term in a sequence serves as the definition for the subsequent term (s). You must specify the initial term in order to establish a recurrence relation.
You then provide a formula that explains how to determine the following term from the previous ones. Take the order 2, 4, 8, 16, 32,... as an example.
Let an be the number of ways to arrange n distinct objects in 5 distinct boxes. It is clear that a1=5.
Let the objects are labelled 1 through n+1. Put the first n objects into the boxes; we can do this in an ways. Then, put the (n+1)th object into one of the 5 boxes. The number of ways to put n distinct objects into 5 distinguishable boxes is 5n.
Hence, the recurrence relation is given by
[tex]( ^{5} _{0} ) 5^{n} - ( ^{5} _{1}) 4^{n} + ( ^{5} _{2}) 3^{n} ( ^{5}_{3} ) 2^{n} + ......... + ( -1)^{6} (^{5} _{4}) 1^{k}[/tex]
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